100 results found for "Math Some Applications Of Trigonometry Word Problems Involving Heights And Distances" in Class 10.
एक ऑफिस में पहले महीने (35) नए आवेदन आए और हर अगले महीने (12) आवेदन अधिक आए। (16)वें महीने कितने आवेदन आएंगे?
In an office (35) new applications are received in the first month and (12) more applications each next month. How many applications will be received in the (16)th month?
#ap
#word-problem
#applications
#nth-term
A (203)
B (211)
C (215)
D (223)
Explanation opens after your attempt
Step 1
Concept
The applications form the AP \(35,47,59,\ldots\) and \(a_{16}=215\). Exam tip: find the (n)th term for a particular month.
Step 2
Why this answer is correct
The correct answer is C. (215). The applications form the AP \(35,47,59,\ldots\) and \(a_{16}=215\). Exam tip: find the (n)th term for a particular month.
Step 3
Exam Tip
आवेदन \(35,47,59,\ldots\) समान्तर श्रेणी में हैं और \(a_{16}=215\)। परीक्षा में खास महीने के लिए (n)वाँ पद निकालें।
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(1800) रुपये कुछ विद्यार्थियों में बराबर बाँटे गए। यदि विद्यार्थी (10) अधिक होते, तो प्रत्येक को (6) रुपये कम मिलते। विद्यार्थियों की मूल संख्या क्या थी?
(1800) rupees were distributed equally among some students. If there were (10) more students, each would get (6) rupees less. What was the original number of students?
#quadratic-equations
#word-problems
#distribution
A (50)
B (60)
C (40)
D (30)
Explanation opens after your attempt
Step 1
Concept
If the number of students is (x), then \(\frac{1800}{x}-\frac{1800}{x+10}=6\). Solving gives (x=50).
Step 2
Why this answer is correct
The correct answer is A. (50). If the number of students is (x), then \(\frac{1800}{x}-\frac{1800}{x+10}=6\). Solving gives (x=50).
Step 3
Exam Tip
यदि विद्यार्थियों की संख्या (x) है, तो \(\frac{1800}{x}-\frac{1800}{x+10}=6\)। हल करने पर (x=50) मिलता है।
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एक व्यक्ति ने (₹1200) को कुछ विद्यार्थियों में बराबर बाँटा। यदि विद्यार्थी (5) अधिक होते, तो प्रत्येक को (₹8) कम मिलते। विद्यार्थियों की मूल संख्या क्या थी?
A person distributed (₹1200) equally among some students. If there were (5) more students, each would get (₹8) less. What was the original number of students?
#quadratic-equations
#word-problems
#distribution
A (25)
B (20)
C (30)
D (15)
Explanation opens after your attempt
Step 1
Concept
If the number of students is (x), then \(\frac{1200}{x}-\frac{1200}{x+5}=8\). Solving gives (x=25).
Step 2
Why this answer is correct
The correct answer is A. (25). If the number of students is (x), then \(\frac{1200}{x}-\frac{1200}{x+5}=8\). Solving gives (x=25).
Step 3
Exam Tip
यदि विद्यार्थियों की संख्या (x) है, तो \(\frac{1200}{x}-\frac{1200}{x+5}=8\)। हल करने पर (x=25) मिलता है।
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कुछ विद्यार्थियों ने चंदा दिया। प्रत्येक विद्यार्थी ने विद्यार्थियों की संख्या से (2) रुपये अधिक दिए और कुल राशि (168) रुपये हुई। विद्यार्थियों की संख्या क्या थी?
Some students donated money. Each student donated (2) rupees more than the number of students and the total amount was (168) rupees. How many students were there?
#quadratic equations
#donation problem
#application
A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
If there are (x) students, then (x(x+2)=168). This gives (x=12).
Step 2
Why this answer is correct
The correct answer is B. (12). If there are (x) students, then (x(x+2)=168). This gives (x=12).
Step 3
Exam Tip
विद्यार्थी (x) हों तो (x(x+2)=168)। इससे (x=12) मिलता है।
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एक व्यापारी ने (1200) रुपये में कुछ पेन खरीदे। यदि प्रति पेन कीमत (10) रुपये कम होती तो (4) पेन अधिक मिलते। मूल पेन संख्या क्या थी?
A trader bought some pens for (1200) rupees. If each pen cost (10) rupees less, he would get (4) more pens. What was the original number of pens?
#quadratic equations
#commerce
#pens
A (16)
B (20)
C (24)
D (30)
Explanation opens after your attempt
Step 1
Concept
Let the original number be (n). Then \(\frac{1200}{n}-\frac{1200}{n+4}=10\). This gives \(10n^2+40n-4800=0\), so (n=20).
Step 2
Why this answer is correct
The correct answer is B. (20). Let the original number be (n). Then \(\frac{1200}{n}-\frac{1200}{n+4}=10\). This gives \(10n^2+40n-4800=0\), so (n=20).
Step 3
Exam Tip
मूल संख्या (n) हो तो \(\frac{1200}{n}-\frac{1200}{n+4}=10\)। इससे \(10n^2+40n-4800=0\) और (n=20) है।
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कुछ विद्यार्थियों ने (540) रुपये बराबर बाँटे। यदि (3) विद्यार्थी कम होते तो प्रत्येक को (30) रुपये अधिक देना पड़ता। वास्तविक विद्यार्थियों की संख्या क्या थी?
Some students shared (540) rupees equally. If there were (3) fewer students, each would pay (30) rupees more. What was the actual number of students?
#quadratic equations
#sharing
#students
A (6)
B (9)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
Let the number of students be (n). Then \(\frac{540}{n-3}-\frac{540}{n}=30\). This gives \(30n^2-90n-1620=0\), so (n=9).
Step 2
Why this answer is correct
The correct answer is B. (9). Let the number of students be (n). Then \(\frac{540}{n-3}-\frac{540}{n}=30\). This gives \(30n^2-90n-1620=0\), so (n=9).
Step 3
Exam Tip
विद्यार्थी (n) हों तो \(\frac{540}{n-3}-\frac{540}{n}=30\)। इससे \(30n^2-90n-1620=0\) और (n=9) मिलता है।
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(720) रुपये में कुछ कॉपियाँ खरीदी गईं। यदि प्रत्येक कॉपी (6) रुपये सस्ती हो जाए तो (4) कॉपियाँ अधिक मिलती हैं। मूल प्रति कॉपी मूल्य क्या था?
Some notebooks are bought for (720) rupees. If each notebook becomes (6) rupees cheaper, (4) more notebooks can be bought. What was the original price per notebook?
#quadratic equations
#price problem
#application
A (30) रुपये / (30) rupees
B (32) रुपये / (32) rupees
C (36) रुपये / (36) rupees
D (40) रुपये / (40) rupees
Explanation opens after your attempt
Correct Answer
C. (36) रुपये / (36) rupees
Step 1
Concept
If the original price is (x), then \(\frac{720}{x-6}-\frac{720}{x}=4\). This gives (x=36).
Step 2
Why this answer is correct
The correct answer is C. (36) रुपये / (36) rupees. If the original price is (x), then \(\frac{720}{x-6}-\frac{720}{x}=4\). This gives (x=36).
Step 3
Exam Tip
मूल मूल्य (x) हो तो \(\frac{720}{x-6}-\frac{720}{x}=4\)। इससे (x=36) मिलता है।
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एक वस्तु पर (1200) रुपये खर्च होते हैं। यदि प्रति वस्तु मूल्य (10) रुपये कम हो जाए तो उसी धन से (4) वस्तुएँ अधिक मिलती हैं। मूल प्रति वस्तु मूल्य क्या था?
A total of (1200) rupees is spent on some items. If the price per item decreases by (10) rupees, (4) more items can be bought for the same money. What was the original price per item?
#quadratic equations
#price quantity
#application
A (50) रुपये / (50) rupees
B (60) रुपये / (60) rupees
C (70) रुपये / (70) rupees
D (80) रुपये / (80) rupees
Explanation opens after your attempt
Correct Answer
B. (60) रुपये / (60) rupees
Step 1
Concept
If original price is (x), then \(\frac{1200}{x-10}-\frac{1200}{x}=4\). Solving gives (x=60).
Step 2
Why this answer is correct
The correct answer is B. (60) रुपये / (60) rupees. If original price is (x), then \(\frac{1200}{x-10}-\frac{1200}{x}=4\). Solving gives (x=60).
Step 3
Exam Tip
मूल मूल्य (x) हो तो \(\frac{1200}{x-10}-\frac{1200}{x}=4\)। हल करने पर (x=60) मिलता है।
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एक दुकानदार (₹800) में कुछ पेन खरीदता है। यदि प्रत्येक पेन की कीमत (₹2) कम होती, तो वह (20) पेन अधिक खरीदता। वास्तविक प्रति पेन कीमत क्या थी?
A shopkeeper buys some pens for (₹800). If each pen cost (₹2) less, he would buy (20) more pens. What was the actual price per pen?
#quadratic equations
#price quantity
#application
A (₹8)
B (₹10)
C (₹12)
D (₹16)
Explanation opens after your attempt
Step 1
Concept
Let the actual price be (x), then \(\frac{800}{x-2}-\frac{800}{x}=20\). This gives \(x^2-2x-80=0\), so (x=10).
Step 2
Why this answer is correct
The correct answer is B. (₹10). Let the actual price be (x), then \(\frac{800}{x-2}-\frac{800}{x}=20\). This gives \(x^2-2x-80=0\), so (x=10).
Step 3
Exam Tip
वास्तविक कीमत (x) हो, तो \(\frac{800}{x-2}-\frac{800}{x}=20\)। इससे \(x^2-2x-80=0\), इसलिए (x=10)।
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एक आयत की लंबाई उसकी चौड़ाई से (5,सेमी) अधिक है और क्षेत्रफल \(150,सेमी^2\) है। आयत की चौड़ाई और लंबाई क्या हैं?
The length of a rectangle is (5,cm) more than its breadth and its area is (150,cm\(^2). What are the breadth and length\)?
#quadratic equations
#word problems
#area
A (10,सेमी) और (15,सेमी) / (10,cm) and (15,cm)
B (12,सेमी) और (17,सेमी) / (12,cm) and (17,cm)
C (8,सेमी) और (13,सेमी) / (8,cm) and (13,cm)
D (9,सेमी) और (14,सेमी) / (9,cm) and (14,cm)
Explanation opens after your attempt
Correct Answer
A. (10,सेमी) और (15,सेमी) / (10,cm) and (15,cm)
Step 1
Concept
If breadth is (x), then (x(x+5)=150), so (x=10). In word problems choose the variable carefully first.
Step 2
Why this answer is correct
The correct answer is A. (10,सेमी) और (15,सेमी) / (10,cm) and (15,cm\(). If breadth is (x), then (x(x+5)=150), so (x=10). In word problems choose the variable carefully first.\)
Step 3
Exam Tip
यदि चौड़ाई (x) है तो (x(x+5)=150) से (x=10) मिलता है। शब्द प्रश्न में पहले चर सही मानें।
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एक संख्या और उसके वर्ग का योग (72) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (72). What is the positive number?
#quadratic-equations
#word-problems
#number-and-square
A (8)
B (9)
C (7)
D (6)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), so \(x^2+x=72\). From \(x^2+x-72=0\), the positive solution is (8).
Step 2
Why this answer is correct
The correct answer is A. (8). Let the number be (x), so \(x^2+x=72\). From \(x^2+x-72=0\), the positive solution is (8).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x^2+x=72\)। \(x^2+x-72=0\) से धनात्मक हल (8) है।
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एक आयताकार बगीचे की लंबाई चौड़ाई से (5 m) अधिक है और क्षेत्रफल \(300 m^2\) है। बगीचे की चौड़ाई क्या होगी?
The length of a rectangular garden is (5 m) more than its breadth and its area is (300 m\(^2). What is the breadth of the garden\)?
#quadratic equations
#word problems
#area
A (15 m)
B (20 m)
C (25 m)
D (30 m)
Explanation opens after your attempt
Step 1
Concept
Let the breadth be (x m\(), so (x(x+5)=300), giving (x=15). In exams, reject the negative dimension.\)
Step 2
Why this answer is correct
The correct answer is A. (15 m). Let the breadth be (x m\(), so (x(x+5)=300), giving (x=15). In exams, reject the negative dimension.\)
Step 3
Exam Tip
मान लें चौड़ाई (x m) है, तब (x(x+5)=300), इसलिए (x=15)। परीक्षा में ऋणात्मक माप को अस्वीकार करें।
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एक दो अंकों की संख्या में दहाई अंक इकाई अंक से (2) कम है और दोनों अंकों का गुणनफल (24) है। संख्या क्या है?
In a two-digit number, the tens digit is (2) less than the units digit and the product of the digits is (24). What is the number?
#quadratic-equations
#word-problems
#two-digit-number
A (46)
B (64)
C (38)
D (83)
Explanation opens after your attempt
Step 1
Concept
If the units digit is (x), then the tens digit is (x-2). From (x(x-2)=24), (x=6), so the number is (46).
Step 2
Why this answer is correct
The correct answer is A. (46). If the units digit is (x), then the tens digit is (x-2). From (x(x-2)=24), (x=6), so the number is (46).
Step 3
Exam Tip
यदि इकाई अंक (x) है, तो दहाई अंक (x-2) है। (x(x-2)=24) से (x=6), इसलिए संख्या (46) है।
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एक दो अंकों की संख्या में दहाई अंक इकाई अंक से (3) अधिक है और दोनों अंकों का गुणनफल (18) है। संख्या क्या है?
In a two-digit number, the tens digit is (3) more than the units digit and the product of the digits is (18). What is the number?
#quadratic-equations
#word-problems
#two-digit-number
A (63)
B (36)
C (92)
D (69)
Explanation opens after your attempt
Step 1
Concept
If the units digit is (x), then the tens digit is (x+3). From (x(x+3)=18), (x=3), so the number is (63).
Step 2
Why this answer is correct
The correct answer is A. (63). If the units digit is (x), then the tens digit is (x+3). From (x(x+3)=18), (x=3), so the number is (63).
Step 3
Exam Tip
यदि इकाई अंक (x) है, तो दहाई अंक (x+3) है। (x(x+3)=18) से (x=3), इसलिए संख्या (63) है।
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एक आयताकार प्लॉट का परिमाप (60) है और क्षेत्रफल (216) है। बड़ी भुजा क्या है?
The perimeter of a rectangular plot is (60) and its area is (216). What is the larger side?
#quadratic-equations
#word-problems
#plot-area
A (18)
B (12)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
The sum of the sides is (30). From (x(30-x)=216), the sides are (18) and (12).
Step 2
Why this answer is correct
The correct answer is A. (18). The sum of the sides is (30). From (x(30-x)=216), the sides are (18) and (12).
Step 3
Exam Tip
भुजाओं का योग (30) है। (x(30-x)=216) से भुजाएँ (18) और (12) मिलती हैं।
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एक (30) मीटर लंबे और (18) मीटर चौड़े मैदान के बाहर चारों ओर समान चौड़ाई का रास्ता है। कुल क्षेत्रफल (748) है। रास्ते की चौड़ाई क्या है?
A field is (30) metres long and (18) metres wide. A uniform path is outside around it. The total area is (748). What is the path width?
#quadratic-equations
#word-problems
#outer-path
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Let the path width be (x), then ((30+2x)(18+2x)=748). At (x=2), \(34\times22=748\).
Step 2
Why this answer is correct
The correct answer is A. (2). Let the path width be (x), then ((30+2x)(18+2x)=748). At (x=2), \(34\times22=748\).
Step 3
Exam Tip
रास्ते की चौड़ाई (x) हो, तो ((30+2x)(18+2x)=748)। (x=2) पर \(34\times22=748\)।
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एक (36) मीटर लंबे और (24) मीटर चौड़े बगीचे में अंदर चारों ओर समान चौड़ाई का रास्ता है। बचा हुआ क्षेत्रफल (540) है। रास्ते की चौड़ाई क्या है?
A garden is (36) metres long and (24) metres wide. A uniform path is inside around it. The remaining area is (540). What is the path width?
#quadratic-equations
#word-problems
#path-area
A (3)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Let the path width be (x), then ((36-2x)(24-2x)=540). Substituting (x=3) gives \(30\times18=540\).
Step 2
Why this answer is correct
The correct answer is A. (3). Let the path width be (x), then ((36-2x)(24-2x)=540). Substituting (x=3) gives \(30\times18=540\).
Step 3
Exam Tip
रास्ते की चौड़ाई (x) हो, तो ((36-2x)(24-2x)=540)। (x=3) रखने पर \(30\times18=540\)।
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एक आयताकार फोटोफ्रेम की बाहरी लंबाई (24) और चौड़ाई (18) है। चारों ओर समान चौड़ाई की पट्टी हटाने पर अंदर का क्षेत्रफल (280) है। पट्टी की चौड़ाई क्या है?
A rectangular photo frame has outer length (24) and breadth (18). After removing a uniform border, the inner area is (280). What is the border width?
#quadratic-equations
#word-problems
#border-frame
A (2)
B (1)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Let the border width be (x), then the inner area is ((24-2x)(18-2x)=280). (x=2) is the correct value.
Step 2
Why this answer is correct
The correct answer is A. (2). Let the border width be (x), then the inner area is ((24-2x)(18-2x)=280). (x=2) is the correct value.
Step 3
Exam Tip
पट्टी की चौड़ाई (x) हो, तो अंदर का क्षेत्रफल ((24-2x)(18-2x)=280)। (x=2) सही मान है।
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एक संख्या में (6) घटाकर उसे उसी संख्या से गुणा करने पर (135) मिलता है। धनात्मक संख्या क्या है?
When (6) is subtracted from a number and the result is multiplied by the same number, the product is (135). What is the positive number?
#quadratic-equations
#word-problems
#number-product
A (15)
B (9)
C (12)
D (18)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x-6)=135). From \(x^2-6x-135=0\), the positive solution is (15).
Step 2
Why this answer is correct
The correct answer is A. (15). If the number is (x), then (x(x-6)=135). From \(x^2-6x-135=0\), the positive solution is (15).
Step 3
Exam Tip
यदि संख्या (x) है, तो (x(x-6)=135)। \(x^2-6x-135=0\) से धनात्मक हल (15) है।
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किस धनात्मक संख्या में (8) जोड़कर उसे मूल संख्या से गुणा करने पर (209) मिलता है?
For which positive number does adding (8) and multiplying by the original number give (209)?
#quadratic-equations
#word-problems
#number-product
A (11)
B (19)
C (8)
D (13)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x+8)=209). From \(x^2+8x-209=0\), (x=11).
Step 2
Why this answer is correct
The correct answer is A. (11). If the number is (x), then (x(x+8)=209). From \(x^2+8x-209=0\), (x=11).
Step 3
Exam Tip
यदि संख्या (x) है, तो (x(x+8)=209)। \(x^2+8x-209=0\) से (x=11) है।
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एक आयत की चौड़ाई (9) है और लंबाई चौड़ाई से (3) कम के (4) गुने के बराबर है। क्षेत्रफल क्या है?
The breadth of a rectangle is (9) and its length is (4) times (3) less than the breadth. What is the area?
#quadratic-equations
#word-problems
#rectangle-expression
A (216)
B (108)
C (144)
D (324)
Explanation opens after your attempt
Step 1
Concept
The breadth is (9), so the length is (4(9-3)=24). The area is \(9\times24=216\).
Step 2
Why this answer is correct
The correct answer is A. (216). The breadth is (9), so the length is (4(9-3)=24). The area is \(9\times24=216\).
Step 3
Exam Tip
चौड़ाई (9) है, इसलिए लंबाई (4(9-3)=24)। क्षेत्रफल \(9\times24=216\) है।
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एक आयताकार कमरे का क्षेत्रफल (432) है और लंबाई चौड़ाई से (6) अधिक है। कमरे की चौड़ाई क्या है?
A rectangular room has area (432) and length (6) more than breadth. What is the breadth of the room?
#quadratic-equations
#word-problems
#room-area
A (18)
B (24)
C (20)
D (16)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+6)=432). This gives (x=18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the breadth is (x), then (x(x+6)=432). This gives (x=18).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+6)=432)। इससे (x=18) मिलता है।
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दो धनात्मक संख्याओं का गुणनफल (378) है और बड़ी संख्या छोटी से (3) अधिक है। छोटी संख्या क्या है?
The product of two positive numbers is (378) and the larger number is (3) more than the smaller. What is the smaller number?
#quadratic-equations
#word-problems
#product-difference
A (18)
B (21)
C (15)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+3). From (x(x+3)=378), (x=18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the smaller number is (x), the larger is (x+3). From (x(x+3)=378), (x=18).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+3) है। (x(x+3)=378) से (x=18) मिलता है।
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दो संख्याओं का योग (26) है और उनके वर्गों का योग (340) है। बड़ी संख्या क्या है?
The sum of two numbers is (26) and the sum of their squares is (340). What is the larger number?
#quadratic-equations
#word-problems
#sum-of-squares
A (14)
B (12)
C (13)
D (16)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (26-x). From (x-2 +(26-x)2 =340), the numbers are (14) and (12).
Step 2
Why this answer is correct
The correct answer is A. (14). If one number is (x), the other is (26-x). From (x-2 +(26-x)2 =340), the numbers are (14) and (12).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (26-x) होगी। (x-2 +(26-x)2 =340) से संख्याएँ (14) और (12) हैं।
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एक आयत का विकर्ण (25) है और लंबाई चौड़ाई से (17) अधिक है। चौड़ाई क्या है?
The diagonal of a rectangle is (25) and its length is (17) more than its breadth. What is the breadth?
#quadratic-equations
#word-problems
#rectangle-diagonal
A (7)
B (24)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), the length is (x+17). From (x-2 +(x+17)2 =252 ), (x=7).
Step 2
Why this answer is correct
The correct answer is A. (7). If the breadth is (x), the length is (x+17). From (x-2 +(x+17)2 =252 ), (x=7).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो लंबाई (x+17) है। (x-2 +(x+17)2 =252 ) से (x=7)।
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तीन लगातार सम पूर्णांकों में पहले और तीसरे का गुणनफल (480) है। बीच वाला सम पूर्णांक क्या है?
In three consecutive even integers, the product of the first and the third is (480). What is the middle even integer?
#quadratic-equations
#word-problems
#even-integers
A (22)
B (20)
C (24)
D (18)
Explanation opens after your attempt
Step 1
Concept
If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=480), (x=22).
Step 2
Why this answer is correct
The correct answer is A. (22). If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=480), (x=22).
Step 3
Exam Tip
यदि बीच वाला (x) है, तो पहले और तीसरे (x-2) तथा (x+2) होंगे। ((x-2)(x+2)=480) से (x=22)।
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तीन लगातार धनात्मक पूर्णांकों में पहले और तीसरे का गुणनफल (195) है। बीच वाला पूर्णांक क्या है?
In three consecutive positive integers, the product of the first and the third is (195). What is the middle integer?
#quadratic-equations
#word-problems
#three-consecutive-integers
A (14)
B (13)
C (15)
D (12)
Explanation opens after your attempt
Step 1
Concept
If the middle integer is (x), the first and third are (x-1) and (x+1). From ((x-1)(x+1)=195), (x=14).
Step 2
Why this answer is correct
The correct answer is A. (14). If the middle integer is (x), the first and third are (x-1) and (x+1). From ((x-1)(x+1)=195), (x=14).
Step 3
Exam Tip
यदि बीच वाला पूर्णांक (x) है, तो पहले और तीसरे (x-1) तथा (x+1) होंगे। ((x-1)(x+1)=195) से (x=14)।
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दो मित्रों की आयु का योग (44) है और उनके आयुओं का गुणनफल (480) है। बड़े मित्र की आयु क्या है?
The sum of ages of two friends is (44) and the product of their ages is (480). What is the age of the older friend?
#quadratic-equations
#word-problems
#ages-product
A (24)
B (20)
C (22)
D (28)
Explanation opens after your attempt
Step 1
Concept
If one age is (x), the other is (44-x). From (x(44-x)=480), the ages are (24) and (20).
Step 2
Why this answer is correct
The correct answer is A. (24). If one age is (x), the other is (44-x). From (x(44-x)=480), the ages are (24) and (20).
Step 3
Exam Tip
यदि एक आयु (x) है, तो दूसरी (44-x) है। (x(44-x)=480) से आयु (24) और (20) मिलती हैं।
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एक आयत का क्षेत्रफल (242) है और उसकी लंबाई चौड़ाई की (2) गुनी है। चौड़ाई क्या है?
The area of a rectangle is (242) and its length is (2) times its breadth. What is the breadth?
#quadratic-equations
#word-problems
#rectangle-ratio
A (11)
B (22)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), the length is (2x). From \(2x^2=242\), (x=11).
Step 2
Why this answer is correct
The correct answer is A. (11). If the breadth is (x), the length is (2x). From \(2x^2=242\), (x=11).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो लंबाई (2x) होगी। \(2x^2=242\) से (x=11) मिलता है।
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एक आयताकार बगीचे की लंबाई चौड़ाई से (4) अधिक है और क्षेत्रफल (360) है। चौड़ाई क्या है?
A rectangular garden has length (4) more than its breadth and area (360). What is the breadth?
#quadratic-equations
#word-problems
#garden-area
A (18)
B (20)
C (16)
D (15)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+4)=360). From (x=18), the breadth is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the breadth is (x), then (x(x+4)=360). From (x=18), the breadth is (18).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+4)=360)। (x=18) से चौड़ाई (18) है।
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एक समकोण त्रिभुज में कर्ण (41) है और एक भुजा दूसरी से (31) अधिक है। छोटी भुजा क्या है?
In a right triangle, the hypotenuse is (41) and one leg is (31) more than the other. What is the smaller leg?
#quadratic-equations
#word-problems
#right-triangle
A (9)
B (40)
C (31)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the smaller leg is (x), the other is (x+31). From (x-2 +(x+31)2 =412 ), (x=9).
Step 2
Why this answer is correct
The correct answer is A. (9). If the smaller leg is (x), the other is (x+31). From (x-2 +(x+31)2 =412 ), (x=9).
Step 3
Exam Tip
यदि छोटी भुजा (x) है, तो दूसरी (x+31) होगी। (x-2 +(x+31)2 =412 ) से (x=9) मिलता है।
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एक सीढ़ी (25) लंबी है और दीवार से पैर की दूरी ऊँचाई से (17) कम है। दीवार पर ऊँचाई क्या है?
A ladder is (25) long and the distance of its foot from the wall is (17) less than the height reached. What is the height on the wall?
#quadratic-equations
#word-problems
#ladder
A (24)
B (7)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
If the height is (x), the distance is (x-17). From (x-2 +(x-17)2 =252 ), (x=24).
Step 2
Why this answer is correct
The correct answer is A. (24). If the height is (x), the distance is (x-17). From (x-2 +(x-17)2 =252 ), (x=24).
Step 3
Exam Tip
यदि ऊँचाई (x) है, तो दूरी (x-17) होगी। (x-2 +(x-17)2 =252 ) से (x=24) मिलता है।
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दो धनात्मक संख्याओं के वर्गों का योग (250) है और उनमें अंतर (4) है। बड़ी संख्या क्या है?
The sum of squares of two positive numbers is (250) and their difference is (4). What is the larger number?
#quadratic-equations
#word-problems
#sum-of-squares
A (13)
B (9)
C (11)
D (15)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+4). From (x-2 +(x+4)2 =250), (x=9), so the larger number is (13).
Step 2
Why this answer is correct
The correct answer is A. (13). If the smaller number is (x), the larger is (x+4). From (x-2 +(x+4)2 =250), (x=9), so the larger number is (13).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+4) है। (x-2 +(x+4)2 =250) से (x=9), इसलिए बड़ी संख्या (13) है।
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दो संख्याओं का अंतर (8) है और गुणनफल (273) है। बड़ी संख्या क्या है?
The difference of two numbers is (8) and their product is (273). What is the larger number?
#quadratic-equations
#word-problems
#difference-product
A (21)
B (13)
C (19)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+8). From (x(x+8)=273), (x=13), so the larger number is (21).
Step 2
Why this answer is correct
The correct answer is A. (21). If the smaller number is (x), the larger is (x+8). From (x(x+8)=273), (x=13), so the larger number is (21).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+8) होगी। (x(x+8)=273) से (x=13), इसलिए बड़ी संख्या (21) है।
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दो संख्याओं का योग (29) है और गुणनफल (204) है। बड़ी संख्या क्या है?
The sum of two numbers is (29) and their product is (204). What is the larger number?
#quadratic-equations
#word-problems
#sum-product
A (17)
B (12)
C (15)
D (29)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (29-x). From (x(29-x)=204), the numbers are (17) and (12).
Step 2
Why this answer is correct
The correct answer is A. (17). If one number is (x), the other is (29-x). From (x(29-x)=204), the numbers are (17) and (12).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (29-x) होगी। (x(29-x)=204) से संख्याएँ (17) और (12) मिलती हैं।
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एक आयत का क्षेत्रफल (216) है और लंबाई चौड़ाई से (6) अधिक है। चौड़ाई क्या है?
The area of a rectangle is (216) and its length is (6) more than its breadth. What is the breadth?
#quadratic-equations
#word-problems
#rectangle
A (12)
B (18)
C (16)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+6)=216). From (x=12), the breadth is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the breadth is (x), then (x(x+6)=216). From (x=12), the breadth is (12).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+6)=216)। (x=12) से चौड़ाई (12) है।
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एक आयत का परिमाप (46) है और क्षेत्रफल (126) है। बड़ी भुजा क्या है?
The perimeter of a rectangle is (46) and its area is (126). What is the larger side?
#quadratic-equations
#word-problems
#perimeter-area
A (14)
B (9)
C (23)
D (12)
Explanation opens after your attempt
Step 1
Concept
The sides are (x) and (23-x). From (x(23-x)=126), the sides are (14) and (9).
Step 2
Why this answer is correct
The correct answer is A. (14). The sides are (x) and (23-x). From (x(23-x)=126), the sides are (14) and (9).
Step 3
Exam Tip
भुजाएँ (x) और (23-x) होंगी। (x(23-x)=126) से भुजाएँ (14) और (9) मिलती हैं।
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एक आयत की लंबाई उसकी चौड़ाई से (5) अधिक है और क्षेत्रफल (204) है। लंबाई क्या है?
The length of a rectangle is (5) more than its breadth and the area is (204). What is the length?
#quadratic-equations
#word-problems
#rectangle-area
A (17)
B (12)
C (19)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+5)=204). With (x=12), the length is (17).
Step 2
Why this answer is correct
The correct answer is A. (17). If the breadth is (x), then (x(x+5)=204). With (x=12), the length is (17).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+5)=204)। (x=12) होने से लंबाई (17) है।
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एक संख्या और उसके व्युत्क्रम का योग \(\frac{10}{3}\) है। बड़ी संख्या क्या है?
The sum of a number and its reciprocal is \(\frac{10}{3}\). What is the larger number?
#quadratic-equations
#word-problems
#reciprocal
A (3)
B \(\frac{1}{3}\)
C (10)
D \(\frac{10}{3}\)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), so \(x+\frac{1}{x}=\frac{10}{3}\). This gives \(3x^2-10x+3=0\), so the larger number is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). Let the number be (x), so \(x+\frac{1}{x}=\frac{10}{3}\). This gives \(3x^2-10x+3=0\), so the larger number is (3).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x+\frac{1}{x}=\frac{10}{3}\)। इससे \(3x^2-10x+3=0\), इसलिए बड़ी संख्या (3) है।
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एक समकोण त्रिभुज में कर्ण (34) है और एक भुजा दूसरी से (14) अधिक है। छोटी भुजा क्या है?
In a right triangle, the hypotenuse is (34) and one side is (14) more than the other. What is the smaller side?
#quadratic-equations
#word-problems
#right-triangle
A (16)
B (30)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
If the smaller side is (x), the other side is (x+14). From (x-2 +(x+14)2 =342 ), (x=16).
Step 2
Why this answer is correct
The correct answer is A. (16). If the smaller side is (x), the other side is (x+14). From (x-2 +(x+14)2 =342 ), (x=16).
Step 3
Exam Tip
यदि छोटी भुजा (x) है, तो दूसरी (x+14) होगी। (x-2 +(x+14)2 =342 ) से (x=16) मिलता है।
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एक (25) मीटर लंबे और (15) मीटर चौड़े मैदान के बाहर समान चौड़ाई का रास्ता है। कुल क्षेत्रफल (651) है। रास्ते की चौड़ाई क्या है?
A field is (25) metres long and (15) metres wide. A uniform path is outside around it. The total area is (651). What is the path width?
#quadratic-equations
#word-problems
#outer-path
A (3)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The equation is ((25+2x)(15+2x)=651). At (x=3), \(31\times21=651\), so the path width is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The equation is ((25+2x)(15+2x)=651). At (x=3), \(31\times21=651\), so the path width is (3).
Step 3
Exam Tip
समीकरण ((25+2x)(15+2x)=651) है। (x=3) पर \(31\times21=651\), इसलिए रास्ते की चौड़ाई (3) है।
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एक (25) मीटर लंबे और (15) मीटर चौड़े मैदान के बाहर चारों ओर समान चौड़ाई का रास्ता है। कुल क्षेत्रफल (589) है। रास्ते की चौड़ाई क्या है?
A field is (25) metres long and (15) metres wide. A uniform path is outside around it. The total area is (589). What is the path width?
#quadratic-equations
#word-problems
#outer-path
A (3)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Let the path width be (x), then ((25+2x)(15+2x)=589). Substituting (x=3) gives \(31\times21=651\), so this option is not valid.
Step 2
Why this answer is correct
The correct answer is A. (3). Let the path width be (x), then ((25+2x)(15+2x)=589). Substituting (x=3) gives \(31\times21=651\), so this option is not valid.
Step 3
Exam Tip
रास्ते की चौड़ाई (x) हो, तो ((25+2x)(15+2x)=589)। (x=3) रखने पर \(31\times21=651\), इसलिए यह विकल्प नहीं है।
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एक (32) मीटर लंबे और (22) मीटर चौड़े बगीचे में अंदर चारों ओर समान चौड़ाई का रास्ता है। बचा हुआ क्षेत्रफल (504) है। रास्ते की चौड़ाई क्या है?
A garden is (32) metres long and (22) metres wide. A uniform path is inside around it. The remaining area is (504). What is the path width?
#quadratic-equations
#word-problems
#path-area
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Let the path width be (x), then ((32-2x)(22-2x)=504). Substituting (x=2) gives \(28\times18=504\), so the width is (2).
Step 2
Why this answer is correct
The correct answer is A. (2). Let the path width be (x), then ((32-2x)(22-2x)=504). Substituting (x=2) gives \(28\times18=504\), so the width is (2).
Step 3
Exam Tip
रास्ते की चौड़ाई (x) हो, तो ((32-2x)(22-2x)=504)। (x=2) रखने पर \(28\times18=504\), इसलिए चौड़ाई (2) है।
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एक (28) मीटर लंबे और (18) मीटर चौड़े बगीचे में अंदर चारों ओर समान चौड़ाई का रास्ता है। बचा हुआ क्षेत्रफल (352) है। रास्ते की चौड़ाई क्या है?
A garden is (28) metres long and (18) metres wide. A uniform path is inside around it. The remaining area is (352). What is the path width?
#quadratic-equations
#word-problems
#path-area
A (2)
B (3)
C (4)
D (1)
Explanation opens after your attempt
Step 1
Concept
If the path width is (x), then ((28-2x)(18-2x)=352). Substituting (x=2) gives \(24\times14=336\), so match the data carefully.
Step 2
Why this answer is correct
The correct answer is A. (2). If the path width is (x), then ((28-2x)(18-2x)=352). Substituting (x=2) gives \(24\times14=336\), so match the data carefully.
Step 3
Exam Tip
यदि रास्ते की चौड़ाई (x) है, तो ((28-2x)(18-2x)=352)। (x=2) रखने पर \(24\times14=336\), इसलिए सही डेटा से मिलान करें।
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एक (30) मीटर लंबे और (20) मीटर चौड़े बगीचे में चारों ओर अंदर समान चौड़ाई का रास्ता है। बचा हुआ क्षेत्रफल (384) है। रास्ते की सही चौड़ाई क्या है?
A garden is (30) metres long and (20) metres wide. A uniform path is inside around it. The remaining area is (384). What is the correct path width?
#quadratic-equations
#word-problems
#path-area
A (3)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The equation is ((30-2x)(20-2x)=384). Substituting (x=3) gives \(24\times14=336\), so recheck the data.
Step 2
Why this answer is correct
The correct answer is A. (3). The equation is ((30-2x)(20-2x)=384). Substituting (x=3) gives \(24\times14=336\), so recheck the data.
Step 3
Exam Tip
समीकरण ((30-2x)(20-2x)=384) है। (x=3) रखने पर \(24\times14=336\) नहीं, इसलिए फिर जाँचें।
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एक (30) मीटर लंबे और (20) मीटर चौड़े बगीचे के चारों ओर अंदर समान चौड़ाई का रास्ता है। बचा हुआ क्षेत्रफल (384) है। रास्ते की चौड़ाई क्या है?
A garden is (30) metres long and (20) metres wide. A uniform path is made inside around it. The remaining area is (384). What is the path width?
#quadratic-equations
#word-problems
#path-area
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Let the path width be (x), then ((30-2x)(20-2x)=384). Substitution must be checked carefully before choosing the option.
Step 2
Why this answer is correct
The correct answer is A. (2). Let the path width be (x), then ((30-2x)(20-2x)=384). Substitution must be checked carefully before choosing the option.
Step 3
Exam Tip
रास्ते की चौड़ाई (x) हो, तो ((30-2x)(20-2x)=384)। (x=2) से बचा क्षेत्रफल \(26\times16=416\) नहीं, इसलिए विकल्पों को जाँचें।
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एक आयताकार फोटोफ्रेम की बाहरी लंबाई (20) और चौड़ाई (16) है। चारों ओर समान चौड़ाई की पट्टी हटाने पर अंदर का क्षेत्रफल (192) है। पट्टी की चौड़ाई क्या है?
A rectangular photo frame has outer length (20) and breadth (16). After removing a uniform border, the inner area is (192). What is the border width?
#quadratic-equations
#word-problems
#border-frame
A (2)
B (1)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Let the border width be (x), then the inner area is ((20-2x)(16-2x)=192). (x=2) is the correct value.
Step 2
Why this answer is correct
The correct answer is A. (2). Let the border width be (x), then the inner area is ((20-2x)(16-2x)=192). (x=2) is the correct value.
Step 3
Exam Tip
पट्टी की चौड़ाई (x) हो, तो अंदर का क्षेत्रफल ((20-2x)(16-2x)=192)। (x=2) सही मान है।
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एक संख्या में (4) घटाकर उसे उसी संख्या से गुणा करने पर (77) मिलता है। धनात्मक संख्या क्या है?
When (4) is subtracted from a number and the result is multiplied by the same number, the product is (77). What is the positive number?
#quadratic-equations
#word-problems
#number-product
A (11)
B (7)
C (13)
D (9)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x-4)=77). From \(x^2-4x-77=0\), the positive solution is (11).
Step 2
Why this answer is correct
The correct answer is A. (11). If the number is (x), then (x(x-4)=77). From \(x^2-4x-77=0\), the positive solution is (11).
Step 3
Exam Tip
यदि संख्या (x) है, तो (x(x-4)=77)। \(x^2-4x-77=0\) से धनात्मक हल (11) है।
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किस धनात्मक संख्या में (6) जोड़कर उसे मूल संख्या से गुणा करने पर (135) मिलता है?
For which positive number does adding (6) and multiplying by the original number give (135)?
#quadratic-equations
#word-problems
#number-product
A (9)
B (15)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x+6)=135). From \(x^2+6x-135=0\), (x=9).
Step 2
Why this answer is correct
The correct answer is A. (9). If the number is (x), then (x(x+6)=135). From \(x^2+6x-135=0\), (x=9).
Step 3
Exam Tip
यदि संख्या (x) है, तो (x(x+6)=135)। \(x^2+6x-135=0\) से (x=9) है।
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एक आयताकार कमरे का क्षेत्रफल (300) है और लंबाई चौड़ाई से (10) अधिक है। कमरे की चौड़ाई क्या है?
A rectangular room has area (300) and length (10) more than breadth. What is the breadth of the room?
#quadratic-equations
#word-problems
#room-area
A (15)
B (20)
C (25)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+10)=300). This gives (x=15).
Step 2
Why this answer is correct
The correct answer is A. (15). If the breadth is (x), then (x(x+10)=300). This gives (x=15).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+10)=300)। इससे (x=15) मिलता है।
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दो धनात्मक संख्याओं का गुणनफल (216) है और बड़ी संख्या छोटी से (6) अधिक है। छोटी संख्या क्या है?
The product of two positive numbers is (216) and the larger number is (6) more than the smaller. What is the smaller number?
#quadratic-equations
#word-problems
#product-difference
A (12)
B (18)
C (10)
D (16)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+6). From (x(x+6)=216), (x=12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the smaller number is (x), the larger is (x+6). From (x(x+6)=216), (x=12).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+6) है। (x(x+6)=216) से (x=12) मिलता है।
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दो संख्याओं का योग (22) है और उनके वर्गों का योग (250) है। बड़ी संख्या क्या है?
The sum of two numbers is (22) and the sum of their squares is (250). What is the larger number?
#quadratic-equations
#word-problems
#sum-of-squares
A (15)
B (7)
C (11)
D (13)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (22-x). From (x-2 +(22-x)2 =250), the numbers are (15) and (7).
Step 2
Why this answer is correct
The correct answer is A. (15). If one number is (x), the other is (22-x). From (x-2 +(22-x)2 =250), the numbers are (15) and (7).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (22-x) होगी। (x-2 +(22-x)2 =250) से संख्याएँ (15) और (7) हैं।
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एक आयत का विकर्ण (13) है और लंबाई चौड़ाई से (7) अधिक है। चौड़ाई क्या है?
The diagonal of a rectangle is (13) and its length is (7) more than its breadth. What is the breadth?
#quadratic-equations
#word-problems
#rectangle-diagonal
A (5)
B (12)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), the length is (x+7). From (x-2 +(x+7)2 =132 ), (x=5).
Step 2
Why this answer is correct
The correct answer is A. (5). If the breadth is (x), the length is (x+7). From (x-2 +(x+7)2 =132 ), (x=5).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो लंबाई (x+7) है। (x-2 +(x+7)2 =132 ) से (x=5)।
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तीन लगातार सम पूर्णांकों में पहले और तीसरे का गुणनफल (320) है। बीच वाला सम पूर्णांक क्या है?
In three consecutive even integers, the product of the first and the third is (320). What is the middle even integer?
#quadratic-equations
#word-problems
#even-integers
A (18)
B (16)
C (20)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=320), (x=18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=320), (x=18).
Step 3
Exam Tip
यदि बीच वाला (x) है, तो पहले और तीसरे (x-2) तथा (x+2) होंगे। ((x-2)(x+2)=320) से (x=18)।
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तीन लगातार धनात्मक पूर्णांकों में पहले और तीसरे का गुणनफल (143) है। बीच वाला पूर्णांक क्या है?
In three consecutive positive integers, the product of the first and the third is (143). What is the middle integer?
#quadratic-equations
#word-problems
#three-consecutive-integers
A (12)
B (11)
C (13)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the middle integer is (x), the first and third are (x-1) and (x+1). From ((x-1)(x+1)=143), (x=12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the middle integer is (x), the first and third are (x-1) and (x+1). From ((x-1)(x+1)=143), (x=12).
Step 3
Exam Tip
यदि बीच वाला पूर्णांक (x) है, तो पहले और तीसरे (x-1) तथा (x+1) होंगे। ((x-1)(x+1)=143) से (x=12)।
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दो मित्रों की आयु का योग (40) है और उनके आयुओं का गुणनफल (375) है। बड़े मित्र की आयु क्या है?
The sum of ages of two friends is (40) and the product of their ages is (375). What is the age of the older friend?
#quadratic-equations
#word-problems
#ages-product
A (25)
B (15)
C (20)
D (30)
Explanation opens after your attempt
Step 1
Concept
If one age is (x), the other is (40-x). From (x(40-x)=375), the ages are (25) and (15).
Step 2
Why this answer is correct
The correct answer is A. (25). If one age is (x), the other is (40-x). From (x(40-x)=375), the ages are (25) and (15).
Step 3
Exam Tip
यदि एक आयु (x) है, तो दूसरी (40-x) है। (x(40-x)=375) से आयु (25) और (15) मिलती हैं।
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एक आयत का क्षेत्रफल (180) है और उसकी लंबाई चौड़ाई से (3) गुनी है। चौड़ाई क्या है?
The area of a rectangle is (180) and its length is (3) times its breadth. What is the breadth?
#quadratic-equations
#word-problems
#rectangle-ratio
A \(2\sqrt{15}\)
B \(3\sqrt{20}\)
C (15)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{15}\)
Step 1
Concept
If the breadth is (x), the length is (3x). From \(3x^2=180\), \(x=2\sqrt{15}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{15}\). If the breadth is (x), the length is (3x). From \(3x^2=180\), \(x=2\sqrt{15}\).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो लंबाई (3x) होगी। \(3x^2=180\) से \(x=2\sqrt{15}\) मिलता है।
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एक आयताकार बगीचे की लंबाई चौड़ाई से (8) अधिक है और क्षेत्रफल (240) है। चौड़ाई क्या है?
A rectangular garden has length (8) more than its breadth and area (240). What is the breadth?
#quadratic-equations
#word-problems
#garden-area
A (12)
B (20)
C (15)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+8)=240). From (x=12), the breadth is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the breadth is (x), then (x(x+8)=240). From (x=12), the breadth is (12).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+8)=240)। (x=12) से चौड़ाई (12) है।
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एक समकोण त्रिभुज में कर्ण (17) है और एक भुजा दूसरी से (7) अधिक है। छोटी भुजा क्या है?
In a right triangle, the hypotenuse is (17) and one leg is (7) more than the other. What is the smaller leg?
#quadratic-equations
#word-problems
#right-triangle
A (8)
B (15)
C (10)
D (7)
Explanation opens after your attempt
Step 1
Concept
If the smaller leg is (x), the other is (x+7). From (x-2 +(x+7)2 =172 ), (x=8).
Step 2
Why this answer is correct
The correct answer is A. (8). If the smaller leg is (x), the other is (x+7). From (x-2 +(x+7)2 =172 ), (x=8).
Step 3
Exam Tip
यदि छोटी भुजा (x) है, तो दूसरी (x+7) होगी। (x-2 +(x+7)2 =172 ) से (x=8) मिलता है।
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एक सीढ़ी (13) लंबी है और दीवार से पैर की दूरी ऊँचाई से (7) कम है। दीवार पर ऊँचाई क्या है?
A ladder is (13) long and the distance of its foot from the wall is (7) less than the height reached. What is the height on the wall?
#quadratic-equations
#word-problems
#ladder
A (12)
B (5)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
If the height is (x), the distance is (x-7). From (x-2 +(x-7)2 =132 ), (x=12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the height is (x), the distance is (x-7). From (x-2 +(x-7)2 =132 ), (x=12).
Step 3
Exam Tip
यदि ऊँचाई (x) है, तो दूरी (x-7) होगी। (x-2 +(x-7)2 =132 ) से (x=12) मिलता है।
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दो धनात्मक संख्याओं के वर्गों का योग (130) है और उनमें अंतर (2) है। बड़ी संख्या क्या है?
The sum of squares of two positive numbers is (130) and their difference is (2). What is the larger number?
#quadratic-equations
#word-problems
#sum-of-squares
A (9)
B (7)
C (11)
D (8)
Explanation opens after your attempt
Step 1
Concept
If the smaller number is (x), the larger is (x+2). From (x-2 +(x+2)2 =130), (x=7), so the larger number is (9).
Step 2
Why this answer is correct
The correct answer is A. (9). If the smaller number is (x), the larger is (x+2). From (x-2 +(x+2)2 =130), (x=7), so the larger number is (9).
Step 3
Exam Tip
यदि छोटी संख्या (x) है, तो बड़ी (x+2) है। (x-2 +(x+2)2 =130) से (x=7), इसलिए बड़ी संख्या (9) है।
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दो संख्याओं का योग (15) है और गुणनफल (54) है। बड़ी संख्या क्या है?
The sum of two numbers is (15) and their product is (54). What is the larger number?
#quadratic-equations
#word-problems
#sum-product
A (9)
B (6)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (15-x). From (x(15-x)=54), the numbers are (9) and (6).
Step 2
Why this answer is correct
The correct answer is A. (9). If one number is (x), the other is (15-x). From (x(15-x)=54), the numbers are (9) and (6).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (15-x) होगी। (x(15-x)=54) से संख्याएँ (9) और (6) मिलती हैं।
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एक आयत का क्षेत्रफल (96) है और लंबाई चौड़ाई से (4) अधिक है। चौड़ाई क्या है?
The area of a rectangle is (96) and its length is (4) more than its breadth. What is the breadth?
#quadratic-equations
#word-problems
#rectangle
A (8)
B (12)
C (10)
D (6)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+4)=96). From (x=8), the breadth is (8).
Step 2
Why this answer is correct
The correct answer is A. (8). If the breadth is (x), then (x(x+4)=96). From (x=8), the breadth is (8).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+4)=96)। (x=8) से आयत की चौड़ाई (8) है।
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एक आयत का परिमाप (34) है और क्षेत्रफल (60) है। बड़ी भुजा क्या है?
The perimeter of a rectangle is (34) and its area is (60). What is the larger side?
#quadratic-equations
#word-problems
#perimeter-area
A (12)
B (5)
C (10)
D (17)
Explanation opens after your attempt
Step 1
Concept
The sides are (x) and (17-x) because (2(l+b)=34). From (x(17-x)=60), the sides are (12) and (5).
Step 2
Why this answer is correct
The correct answer is A. (12). The sides are (x) and (17-x) because (2(l+b)=34). From (x(17-x)=60), the sides are (12) and (5).
Step 3
Exam Tip
भुजाएँ (x) और (17-x) होंगी क्योंकि (2(l+b)=34)। (x(17-x)=60) से भुजाएँ (12) और (5) मिलती हैं।
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एक आयत की लंबाई उसकी चौड़ाई से (3) अधिक है और क्षेत्रफल (70) है। लंबाई क्या है?
The length of a rectangle is (3) more than its breadth and the area is (70). What is the length?
#quadratic-equations
#word-problems
#rectangle-area
A (10)
B (7)
C (13)
D (9)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+3)=70). With (x=7), the length is (10).
Step 2
Why this answer is correct
The correct answer is A. (10). If the breadth is (x), then (x(x+3)=70). With (x=7), the length is (10).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+3)=70)। (x=7) होने से लंबाई (10) है।
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एक संख्या और उसके व्युत्क्रम का योग \(\frac{5}{2}\) है। बड़ी संख्या क्या है?
The sum of a number and its reciprocal is \(\frac{5}{2}\). What is the larger number?
#quadratic-equations
#word-problems
#reciprocal
A (2)
B \(\frac{1}{2}\)
C (5)
D \(\frac{5}{2}\)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), so \(x+\frac{1}{x}=\frac{5}{2}\). This gives \(2x^2-5x+2=0\), so the larger number is (2).
Step 2
Why this answer is correct
The correct answer is A. (2). Let the number be (x), so \(x+\frac{1}{x}=\frac{5}{2}\). This gives \(2x^2-5x+2=0\), so the larger number is (2).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x+\frac{1}{x}=\frac{5}{2}\)। इससे \(2x^2-5x+2=0\), इसलिए बड़ी संख्या (2) है।
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दो मजदूर मिलकर एक काम (6 days) में पूरा करते हैं। पहला मजदूर अकेले दूसरे से (5 days) कम समय लेता है। पहला मजदूर अकेले काम कितने दिनों में करेगा?
Two workers together complete a work in (6 days). The first worker alone takes (5 days) less than the second worker. In how many days will the first worker alone complete the work?
#quadratic equations
#work and time
#word problems
A (10 days)
B (12 days)
C (15 days)
D (18 days)
Explanation opens after your attempt
Correct Answer
A. (10 days)
Step 1
Concept
Let the first worker's time be (x days\(), then (\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}). This gives (x^2-7x-30=0), so (x=10).\)
Step 2
Why this answer is correct
The correct answer is A. (10 days). Let the first worker's time be (x days\(), then (\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}). This gives (x^2-7x-30=0), so (x=10).\)
Step 3
Exam Tip
पहले मजदूर का समय (x days) मानें, तब \(\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}\)। \(इससे (x^2-7x-30=0), इसलिए (x=10) है\)।
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एक नाव शांत जल में (20) किलोमीटर प्रति घंटा चलती है। धारा की गति (x) है। (48) किलोमीटर धारा के साथ और (32) किलोमीटर धारा के विरुद्ध जाने में कुल (4) घंटे लगते हैं। (x) क्या है?
A boat moves at (20) kilometres per hour in still water. The stream speed is (x). It takes (4) hours to go (48) kilometres downstream and (32) kilometres upstream. What is (x)?
#quadratic-equations
#word-problems
#boat-stream
A (4)
B (3)
C (5)
D (2)
Explanation opens after your attempt
Step 1
Concept
The equation is \(\frac{48}{20+x}+\frac{32}{20-x}=4\). Substituting (x=4) gives time (2+2=4) hours.
Step 2
Why this answer is correct
The correct answer is A. (4). The equation is \(\frac{48}{20+x}+\frac{32}{20-x}=4\). Substituting (x=4) gives time (2+2=4) hours.
Step 3
Exam Tip
समीकरण \(\frac{48}{20+x}+\frac{32}{20-x}=4\) है। (x=4) रखने पर समय (2+2=4) घंटे मिलता है।
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एक नाव शांत जल में (15) किलोमीटर प्रति घंटा चलती है। धारा की गति (x) है। (36) किलोमीटर धारा के साथ और (24) किलोमीटर धारा के विरुद्ध जाने में कुल (4) घंटे लगते हैं। (x) क्या है?
A boat moves at (15) kilometres per hour in still water. The stream speed is (x). It takes (4) hours to go (36) kilometres downstream and (24) kilometres upstream. What is (x)?
#quadratic-equations
#word-problems
#boat-stream
A (3)
B (2)
C (5)
D (4)
Explanation opens after your attempt
Step 1
Concept
The equation is \(\frac{36}{15+x}+\frac{24}{15-x}=4\). Substituting (x=3) gives time (2+2=4) hours.
Step 2
Why this answer is correct
The correct answer is A. (3). The equation is \(\frac{36}{15+x}+\frac{24}{15-x}=4\). Substituting (x=3) gives time (2+2=4) hours.
Step 3
Exam Tip
समीकरण \(\frac{36}{15+x}+\frac{24}{15-x}=4\) है। (x=3) रखने पर समय (2+2=4) घंटे मिलता है।
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दो क्रमागत धनात्मक पूर्णांकों का गुणनफल (552) है। वे पूर्णांक कौन-से हैं?
The product of two consecutive positive integers is (552). Which are the integers?
#quadratic equations
#word problems
#consecutive integers
A (22) और (23) / (22) and (23)
B (23) और (24) / (23) and (24)
C (24) और (25) / (24) and (25)
D (21) और (22) / (21) and (22)
Explanation opens after your attempt
Correct Answer
B. (23) और (24) / (23) and (24)
Step 1
Concept
Let the numbers be (x) and (x+1). From (x(x+1)=552), we get (x=23).
Step 2
Why this answer is correct
The correct answer is B. (23) और (24) / (23) and (24). Let the numbers be (x) and (x+1). From (x(x+1)=552), we get (x=23).
Step 3
Exam Tip
मान लें संख्याएँ (x) और (x+1) हैं। (x(x+1)=552) से (x=23) मिलता है।
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एक ट्रेन (300 km) दूरी तय करती है। यदि उसकी चाल (10 km/h) अधिक होती, तो समय (1 h) कम लगता। ट्रेन की वास्तविक चाल क्या थी?
A train covers a distance of (300 km). If its speed were (10 km/h) more, it would take (1 h) less. What was the actual speed of the train?
#quadratic equations
#speed time distance
#word problems
A \((40\text{ km\) / h})
B \((50\text{ km\) / h})
C \((60\text{ km\) / h})
D \((75\text{ km\) / h})
Explanation opens after your attempt
Correct Answer
B. \((50\text{ km\) / h})
Step 1
Concept
Let the actual speed be (x km/h\(), then (\frac{300}{x}-\frac{300}{x+10}=1). This gives (x^2+10x-3000=0), so the positive root is (x=50).\)
Step 2
Why this answer is correct
The correct answer is B. (50 km / h). Let the actual speed be (x km/h\(), then (\frac{300}{x}-\frac{300}{x+10}=1). This gives (x^2+10x-3000=0), so the positive root is (x=50).\)
Step 3
Exam Tip
वास्तविक चाल (x km/h) मानें, तब \(\frac{300}{x}-\frac{300}{x+10}=1\)। \(इससे (x^2+10x-3000=0), इसलिए धनात्मक मूल (x=50) है\)।
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दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (1513) है। छोटा पूर्णांक क्या है?
The sum of squares of two consecutive positive integers is (1513). What is the smaller integer?
#quadratic equations
#word problems
#sum of squares
A (25)
B (26)
C (27)
D (28)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x-2 +(x+1)2 =1513), giving (x=27). Write consecutive integers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is C. (27). If the smaller integer is (x), then (x-2 +(x+1)2 =1513), giving (x=27). Write consecutive integers as (x) and (x+1).
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x-2 +(x+1)2 =1513), जिससे (x=27) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।
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दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (1201) है। छोटा पूर्णांक क्या है?
The sum of squares of two consecutive positive integers is (1201). What is the smaller integer?
#quadratic equations
#word problems
#sum of squares
A (22)
B (23)
C (24)
D (25)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x-2 +(x+1)2 =1201), giving (x=24). Write consecutive integers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is C. (24). If the smaller integer is (x), then (x-2 +(x+1)2 =1201), giving (x=24). Write consecutive integers as (x) and (x+1).
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x-2 +(x+1)2 =1201), जिससे (x=24) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।
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दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (841) है। छोटा पूर्णांक क्या है?
The sum of squares of two consecutive positive integers is (841). What is the smaller integer?
#quadratic equations
#word problems
#sum of squares
A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x-2 +(x+1)2 =841), giving (x=20). Write consecutive numbers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is C. (20). If the smaller integer is (x), then (x-2 +(x+1)2 =841), giving (x=20). Write consecutive numbers as (x) and (x+1).
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x-2 +(x+1)2 =841), जिससे (x=20) मिलता है। लगातार संख्याओं को (x) और (x+1) लिखें।
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एक काम में व्यक्ति (A), व्यक्ति (B) से (5) दिन कम समय लेता है। दोनों मिलकर काम (6) दिन में पूरा करते हैं। (B) अकेले कितने दिन लेगा?
In a work problem, person (A) takes (5) days less than person (B). Together they complete the work in (6) days. How many days will (B) alone take?
#quadratic-equations
#word-problems
#work-time
A (15)
B (10)
C (20)
D (12)
Explanation opens after your attempt
Step 1
Concept
If (B) alone takes (x) days, then (A) takes (x-5) days. From \(\frac{1}{x}+\frac{1}{x-5}=\frac{1}{6}\), (x=15).
Step 2
Why this answer is correct
The correct answer is A. (15). If (B) alone takes (x) days, then (A) takes (x-5) days. From \(\frac{1}{x}+\frac{1}{x-5}=\frac{1}{6}\), (x=15).
Step 3
Exam Tip
यदि (B) अकेले (x) दिन लेता है, तो (A) (x-5) दिन लेता है। \(\frac{1}{x}+\frac{1}{x-5}=\frac{1}{6}\) से (x=15)।
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एक प्रतियोगिता में प्रत्येक टीम प्रत्येक अन्य टीम से एक मैच खेलती है। कुल मैच (28) हैं। टीमों की संख्या क्या है?
In a tournament, each team plays one match with every other team. The total number of matches is (28). What is the number of teams?
#quadratic-equations
#word-problems
#tournament
A (8)
B (7)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the number of teams is (n), then (\frac{n(n-1)}{2}=28). Solving gives (n=8).
Step 2
Why this answer is correct
The correct answer is A. (8). If the number of teams is (n), then (\frac{n(n-1)}{2}=28). Solving gives (n=8).
Step 3
Exam Tip
यदि टीमों की संख्या (n) है, तो (\frac{n(n-1)}{2}=28)। हल करने पर (n=8) मिलता है।
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एक समूह में प्रत्येक व्यक्ति प्रत्येक अन्य व्यक्ति से एक बार हाथ मिलाता है। कुल हाथ मिलाने की संख्या (66) है। व्यक्तियों की संख्या क्या है?
In a group, each person shakes hands with every other person once. The total number of handshakes is (66). What is the number of persons?
#quadratic-equations
#word-problems
#handshake
A (12)
B (11)
C (13)
D (10)
Explanation opens after your attempt
Step 1
Concept
If the number of persons is (n), then (\frac{n(n-1)}{2}=66). This gives (n=12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the number of persons is (n), then (\frac{n(n-1)}{2}=66). This gives (n=12).
Step 3
Exam Tip
यदि व्यक्तियों की संख्या (n) है, तो (\frac{n(n-1)}{2}=66)। इससे (n=12) मिलता है।
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एक परीक्षा में (x) सही प्रश्नों के लिए अंक (x(30-x)) मिलते हैं। यदि अंक (216) हैं, तो (x) का बड़ा मान क्या है?
In an exam, (x) correct questions give marks (x(30-x)). If the marks are (216), what is the larger value of (x)?
#quadratic-equations
#word-problems
#exam-scenario
A (18)
B (12)
C (15)
D (24)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(30-x)=216). From \(x^2-30x+216=0\), (x=12) or (18); the larger value is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). The equation is (x(30-x)=216). From \(x^2-30x+216=0\), (x=12) or (18); the larger value is (18).
Step 3
Exam Tip
समीकरण (x(30-x)=216) है। \(x^2-30x+216=0\) से (x=12) या (18); बड़ा मान (18) है।
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एक दुकानदार (x) रुपये प्रति वस्तु के हिसाब से (80-x) वस्तुएँ बेचता है। कुल आय (1500) है। (x) का छोटा मान क्या है?
A shopkeeper sells (80-x) items at (x) rupees per item. The total revenue is (1500). What is the smaller value of (x)?
#quadratic-equations
#word-problems
#sales-revenue
A (30)
B (50)
C (40)
D (20)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(80-x)=1500). From \(x^2-80x+1500=0\), (x=30) or (50), so the smaller value is (30).
Step 2
Why this answer is correct
The correct answer is A. (30). The equation is (x(80-x)=1500). From \(x^2-80x+1500=0\), (x=30) or (50), so the smaller value is (30).
Step 3
Exam Tip
समीकरण (x(80-x)=1500) है। \(x^2-80x+1500=0\) से (x=30) या (50), छोटा मान (30) है।
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एक पोस्टर का क्षेत्रफल (216) है। लंबाई चौड़ाई से (6) अधिक है। चौड़ाई क्या है?
A poster has area (216). Its length is (6) more than its breadth. What is the breadth?
#quadratic-equations
#word-problems
#poster-area
A (12)
B (18)
C (9)
D (15)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+6)=216). Since (x=12), the breadth is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the breadth is (x), then (x(x+6)=216). Since (x=12), the breadth is (12).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+6)=216)। (x=12) होने से चौड़ाई (12) है।
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एक संख्या का वर्ग उसके (15) गुने से (54) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (54) more than (15) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (18)
B (3)
C (15)
D (54)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=15x+54\)। \(x^2-15x-54=0\) से धनात्मक संख्या (18) है।
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एक वर्गाकार पार्क का क्षेत्रफल (196) है। उसकी भुजा में (4) बढ़ाने पर नया क्षेत्रफल कितना होगा?
A square park has area (196). If its side is increased by (4), what will be the new area?
#quadratic-equations
#word-problems
#square-area
A (324)
B (256)
C (400)
D (289)
Explanation opens after your attempt
Step 1
Concept
If the original side is (x), then \(x^2=196\), so (x=14). The new side is (18), and the new area is \(18^2=324\).
Step 2
Why this answer is correct
The correct answer is A. (324). If the original side is (x), then \(x^2=196\), so (x=14). The new side is (18), and the new area is \(18^2=324\).
Step 3
Exam Tip
मूल भुजा (x) हो तो \(x^2=196\), इसलिए (x=14)। नई भुजा (18) है और नया क्षेत्रफल \(18^2=324\)।
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एक पिता की आयु पुत्र की आयु से (28) अधिक है। (4) वर्ष बाद दोनों आयुओं का गुणनफल (960) होगा। पुत्र की वर्तमान आयु क्या है?
A father's age is (28) more than his son's age. After (4) years, the product of their ages will be (960). What is the son's present age?
#quadratic-equations
#word-problems
#age
A (16)
B (20)
C (12)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the son's present age is (x), then ((x+4)(x+32)=960). This gives (x=16).
Step 2
Why this answer is correct
The correct answer is A. (16). If the son's present age is (x), then ((x+4)(x+32)=960). This gives (x=16).
Step 3
Exam Tip
यदि पुत्र की वर्तमान आयु (x) है, तो ((x+4)(x+32)=960)। इससे (x=16) मिलता है।
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(1680) रुपये एक कक्षा में बराबर बाँटे गए। यदि विद्यार्थी (4) कम होते, तो प्रत्येक को (10) रुपये अधिक मिलते। मूल विद्यार्थी संख्या क्या है?
(1680) rupees were distributed equally in a class. If there were (4) fewer students, each would get (10) rupees more. What is the original number of students?
#quadratic-equations
#word-problems
#money-distribution
A (28)
B (24)
C (32)
D (20)
Explanation opens after your attempt
Step 1
Concept
If there are (x) students, then \(\frac{1680}{x-4}-\frac{1680}{x}=10\). Solving gives (x=28).
Step 2
Why this answer is correct
The correct answer is A. (28). If there are (x) students, then \(\frac{1680}{x-4}-\frac{1680}{x}=10\). Solving gives (x=28).
Step 3
Exam Tip
यदि विद्यार्थी (x) हैं, तो \(\frac{1680}{x-4}-\frac{1680}{x}=10\)। हल करने पर (x=28) मिलता है।
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एक व्यक्ति (300) किलोमीटर यात्रा करता है। गति (10) किलोमीटर प्रति घंटा कम करने पर समय (1) घंटा बढ़ जाता है। मूल गति क्या है?
A person travels (300) kilometres. If the speed is reduced by (10) kilometres per hour, the time increases by (1) hour. What is the original speed?
#quadratic-equations
#word-problems
#speed-change
A (60)
B (50)
C (40)
D (30)
Explanation opens after your attempt
Step 1
Concept
Let the original speed be (x), then \(\frac{300}{x-10}-\frac{300}{x}=1\). Solving gives (x=60).
Step 2
Why this answer is correct
The correct answer is A. (60). Let the original speed be (x), then \(\frac{300}{x-10}-\frac{300}{x}=1\). Solving gives (x=60).
Step 3
Exam Tip
मूल गति (x) हो, तो \(\frac{300}{x-10}-\frac{300}{x}=1\)। हल करने पर (x=60) मिलता है।
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एक ट्रेन (360) किलोमीटर दूरी तय करती है। गति (15) किलोमीटर प्रति घंटा बढ़ाने पर समय (2) घंटे कम हो जाता है। मूल गति क्या है?
A train covers (360) kilometres. If its speed is increased by (15) kilometres per hour, the time decreases by (2) hours. What is the original speed?
#quadratic-equations
#word-problems
#speed-time
A (45)
B (60)
C (30)
D (40)
Explanation opens after your attempt
Step 1
Concept
Let the original speed be (x), then \(\frac{360}{x}-\frac{360}{x+15}=2\). Solving gives (x=45).
Step 2
Why this answer is correct
The correct answer is A. (45). Let the original speed be (x), then \(\frac{360}{x}-\frac{360}{x+15}=2\). Solving gives (x=45).
Step 3
Exam Tip
मूल गति (x) हो, तो \(\frac{360}{x}-\frac{360}{x+15}=2\)। हल करने पर (x=45) मिलता है।
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एक किसान (384) वर्ग मीटर क्षेत्रफल वाला आयताकार खेत बनाता है। लंबाई चौड़ाई से (8) अधिक है। चौड़ाई क्या है?
A farmer makes a rectangular field of area (384) square metres. The length is (8) more than the breadth. What is the breadth?
#quadratic-equations
#word-problems
#field-area
A (16)
B (24)
C (18)
D (12)
Explanation opens after your attempt
Step 1
Concept
If the breadth is (x), then (x(x+8)=384). With (x=16), the breadth is (16).
Step 2
Why this answer is correct
The correct answer is A. (16). If the breadth is (x), then (x(x+8)=384). With (x=16), the breadth is (16).
Step 3
Exam Tip
यदि चौड़ाई (x) है, तो (x(x+8)=384)। (x=16) होने से चौड़ाई (16) है।
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एक वस्तु को (x) रुपये में बेचने पर कुल आय (x(70-x)) है। यदि कुल आय (1200) है, तो (x) का बड़ा मान क्या है?
An item sold at (x) rupees gives total revenue (x(70-x)). If the total revenue is (1200), what is the larger value of (x)?
#quadratic-equations
#word-problems
#revenue
A (40)
B (30)
C (35)
D (50)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(70-x)=1200). This gives (x=30) or (40); the larger value is (40).
Step 2
Why this answer is correct
The correct answer is A. (40). The equation is (x(70-x)=1200). This gives (x=30) or (40); the larger value is (40).
Step 3
Exam Tip
समीकरण (x(70-x)=1200) है। इससे (x=30) या (40); बड़ा मान (40) है।
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एक संख्या के वर्ग में (17) घटाने पर (127) मिलता है। धनात्मक संख्या क्या है?
When (17) is subtracted from the square of a number, the result is (127). What is the positive number?
#quadratic-equations
#word-problems
#square-root
A (12)
B (10)
C (14)
D (8)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x^2-17=127\)। इससे \(x^2=144\), इसलिए धनात्मक संख्या (12) है।
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एक संख्या को उसके अगले पूर्णांक से गुणा करने पर (552) मिलता है। संख्या क्या है?
A number multiplied by its next integer gives (552). What is the number?
#quadratic-equations
#word-problems
#next-integer
A (23)
B (24)
C (22)
D (21)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then (x(x+1)=552). Since \(23\times24=552\), the number is (23).
Step 2
Why this answer is correct
The correct answer is A. (23). If the number is (x), then (x(x+1)=552). Since \(23\times24=552\), the number is (23).
Step 3
Exam Tip
यदि संख्या (x) है, तो (x(x+1)=552)। \(23\times24=552\), इसलिए संख्या (23) है।
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एक संख्या का वर्ग उस संख्या के (11) गुने से (42) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (42) more than (11) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (14)
B (3)
C (11)
D (42)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).
Step 2
Why this answer is correct
The correct answer is A. (14). If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=11x+42\)। \(x^2-11x-42=0\) से धनात्मक हल (14) है।
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एक वर्ग का क्षेत्रफल उसके परिमाप से (96) अधिक है। वर्ग की भुजा क्या है?
The area of a square is (96) more than its perimeter. What is the side of the square?
#quadratic-equations
#word-problems
#square
A (12)
B (8)
C (16)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the side is (x), then \(x^2=4x+96\). This gives \(x^2-4x-96=0\), so the positive side is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the side is (x), then \(x^2=4x+96\). This gives \(x^2-4x-96=0\), so the positive side is (12).
Step 3
Exam Tip
यदि भुजा (x) है, तो \(x^2=4x+96\)। इससे \(x^2-4x-96=0\), इसलिए धनात्मक भुजा (12) है।
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दो लगातार धनात्मक सम पूर्णांकों का गुणनफल (288) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive even integers is (288). What is the larger integer?
#quadratic-equations
#word-problems
#even-integers
A (18)
B (16)
C (20)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the smaller even integer is (x), then (x(x+2)=288). Since (x=16), the larger integer is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the smaller even integer is (x), then (x(x+2)=288). Since (x=16), the larger integer is (18).
Step 3
Exam Tip
यदि छोटा सम पूर्णांक (x) है, तो (x(x+2)=288)। (x=16) होने से बड़ा पूर्णांक (18) है।
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दो लगातार धनात्मक विषम पूर्णांकों का गुणनफल (399) है। छोटा पूर्णांक क्या है?
The product of two consecutive positive odd integers is (399). What is the smaller integer?
#quadratic-equations
#word-problems
#odd-integers
A (19)
B (21)
C (17)
D (23)
Explanation opens after your attempt
Step 1
Concept
If the smaller odd integer is (x), then (x(x+2)=399). Since \(19\times21=399\), the smaller integer is (19).
Step 2
Why this answer is correct
The correct answer is A. (19). If the smaller odd integer is (x), then (x(x+2)=399). Since \(19\times21=399\), the smaller integer is (19).
Step 3
Exam Tip
यदि छोटा विषम पूर्णांक (x) है, तो (x(x+2)=399)। \(19\times21=399\), इसलिए छोटा पूर्णांक (19) है।
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दो लगातार धनात्मक पूर्णांकों का गुणनफल (306) है। बड़ा पूर्णांक क्या है?
The product of two consecutive positive integers is (306). What is the larger integer?
#quadratic-equations
#word-problems
#consecutive-integers
A (18)
B (17)
C (19)
D (16)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x(x+1)=306). When (x=17), the larger integer is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the smaller integer is (x), then (x(x+1)=306). When (x=17), the larger integer is (18).
Step 3
Exam Tip
यदि छोटा पूर्णांक (x) है, तो (x(x+1)=306)। (x=17) होने पर बड़ा पूर्णांक (18) है।
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दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (365) है। छोटा पूर्णांक क्या है?
The sum of squares of two consecutive positive integers is (365). What is the smaller integer?
#quadratic equations
#word problems
#sum of squares
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the smaller integer is (x), then (x-2 +(x+1)2 =365), giving (x=13). Write consecutive integers as (x) and (x+1).
Step 2
Why this answer is correct
The correct answer is C. (13). If the smaller integer is (x), then (x-2 +(x+1)2 =365), giving (x=13). Write consecutive integers as (x) and (x+1).
Step 3
Exam Tip
छोटा पूर्णांक (x) हो तो (x-2 +(x+1)2 =365), जिससे (x=13) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।
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एक बस (180) किलोमीटर दूरी तय करती है। गति (15) किलोमीटर प्रति घंटा बढ़ाने पर समय (1) घंटा कम हो जाता है। मूल गति क्या है?
A bus covers (180) kilometres. If its speed is increased by (15) kilometres per hour, the time decreases by (1) hour. What is the original speed?
#quadratic-equations
#word-problems
#speed-time
A (45)
B (60)
C (30)
D (40)
Explanation opens after your attempt
Step 1
Concept
Let the original speed be (x), then \(\frac{180}{x}-\frac{180}{x+15}=1\). Solving gives (x=45).
Step 2
Why this answer is correct
The correct answer is A. (45). Let the original speed be (x), then \(\frac{180}{x}-\frac{180}{x+15}=1\). Solving gives (x=45).
Step 3
Exam Tip
मूल गति (x) हो, तो \(\frac{180}{x}-\frac{180}{x+15}=1\)। हल करने पर (x=45) मिलता है।
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एक समूह में प्रत्येक व्यक्ति प्रत्येक अन्य व्यक्ति से एक बार हाथ मिलाता है। कुल हाथ मिलाने की संख्या (45) है। व्यक्तियों की संख्या क्या है?
In a group, each person shakes hands with every other person once. The total number of handshakes is (45). What is the number of persons?
#quadratic-equations
#word-problems
#handshake
A (10)
B (9)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
If the number of persons is (n), then the number of handshakes is (\frac{n(n-1)}{2}=45). This gives (n=10).
Step 2
Why this answer is correct
The correct answer is A. (10). If the number of persons is (n), then the number of handshakes is (\frac{n(n-1)}{2}=45). This gives (n=10).
Step 3
Exam Tip
यदि व्यक्तियों की संख्या (n) है, तो हाथ मिलाने की संख्या (\frac{n(n-1)}{2}=45)। इससे (n=10) मिलता है।
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एक परीक्षा में (x) सही प्रश्नों के लिए अंक (x(20-x)) मिलते हैं। यदि अंक (96) हैं, तो (x) का बड़ा मान क्या है?
In an exam, (x) correct questions give marks (x(20-x)). If the marks are (96), what is the larger value of (x)?
#quadratic-equations
#word-problems
#exam-scenario
A (12)
B (8)
C (10)
D (16)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(20-x)=96). From \(x^2-20x+96=0\), (x=8) or (12); the larger value is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). The equation is (x(20-x)=96). From \(x^2-20x+96=0\), (x=8) or (12); the larger value is (12).
Step 3
Exam Tip
समीकरण (x(20-x)=96) है। \(x^2-20x+96=0\) से (x=8) या (12); बड़ा मान (12) है।
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एक दुकानदार (x) रुपये प्रति वस्तु के हिसाब से (60-x) वस्तुएँ बेचता है। कुल आय (875) है। (x) का छोटा मान क्या है?
A shopkeeper sells (60-x) items at (x) rupees per item. The total revenue is (875). What is the smaller value of (x)?
#quadratic-equations
#word-problems
#sales-revenue
A (25)
B (35)
C (30)
D (20)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(60-x)=875). From \(x^2-60x+875=0\), (x=25) or (35), so the smaller value is (25).
Step 2
Why this answer is correct
The correct answer is A. (25). The equation is (x(60-x)=875). From \(x^2-60x+875=0\), (x=25) or (35), so the smaller value is (25).
Step 3
Exam Tip
समीकरण (x(60-x)=875) है। \(x^2-60x+875=0\) से (x=25) या (35), छोटा मान (25) है।
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