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quadratic equations MCQ Questions for Class 10

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1750 questions tagged with quadratic equations.

Question 31/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक समकोण त्रिभुज में लम्ब आधार से (7) सेमी अधिक है और कर्ण (25) सेमी है। आधार कितना है?

In a right triangle, the perpendicular is (7) cm more than the base and the hypotenuse is (25) cm. What is the base?

Explanation opens after your attempt
Correct Answer

A. (15) सेमी(15) cm

Step 1

Concept

The base is (x) and perpendicular is (x+7). From (x-2+(x+7)2=252), (x=15).

Step 2

Why this answer is correct

The correct answer is A. (15) सेमी / (15) cm. The base is (x) and perpendicular is (x+7). From (x-2+(x+7)2=252), (x=15).

Step 3

Exam Tip

आधार (x) और लम्ब (x+7) है। (x-2+(x+7)2=252) से (x=15) मिलता है।

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Question 32/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक आयत की लंबाई और चौड़ाई का अंतर (7) सेमी है तथा क्षेत्रफल (330) वर्ग सेमी है। परिमाप कितना है?

The difference between the length and breadth of a rectangle is (7) cm and its area is (330) square cm. What is its perimeter?

Explanation opens after your attempt
Correct Answer

B. (74) सेमी(74) cm

Step 1

Concept

If breadth is (x), length is (x+7). From (x(x+7)=330), (x=15), so perimeter is (2(15+22)=74).

Step 2

Why this answer is correct

The correct answer is B. (74) सेमी / (74) cm. If breadth is (x), length is (x+7). From (x(x+7)=330), (x=15), so perimeter is (2(15+22)=74).

Step 3

Exam Tip

चौड़ाई (x) हो तो लंबाई (x+7) है। (x(x+7)=330) से (x=15) और परिमाप (2(15+22)=74) है।

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Question 33/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक आयताकार पार्क का क्षेत्रफल (576) वर्ग मीटर अधिकतम है जब दो समान चौड़ाइयों और एक लंबाई के लिए कुल बाड़ (96) मीटर है। चौड़ाई क्या है?

A rectangular park has maximum area (576) square m when the total fencing for two equal breadths and one length is (96) m. What is the breadth?

Explanation opens after your attempt
Correct Answer

C. (24) मीटर(24) m

Step 1

Concept

For fencing on three sides, (l+2b=96). (A=b(96-2b)) is maximum when (b=24).

Step 2

Why this answer is correct

The correct answer is C. (24) मीटर / (24) m. For fencing on three sides, (l+2b=96). (A=b(96-2b)) is maximum when (b=24).

Step 3

Exam Tip

तीन ओर की बाड़ में (l+2b=96) है। (A=b(96-2b)) अधिकतम तब होता है जब (b=24)।

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Question 34/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक किसान के पास (100) मीटर बाड़ है जिससे वह दीवार के साथ आयताकार खेत के तीन ओर घेरता है। अधिकतम क्षेत्रफल कब मिलेगा?

A farmer has (100) m fencing to enclose three sides of a rectangular field along a wall. When will the maximum area occur?

Explanation opens after your attempt
Correct Answer

B. चौड़ाई (25) मीटरBreadth (25) m

Step 1

Concept

If breadth is (x), length is (100-2x) and area is (A=x(100-2x)). For maximum area, \(x=\frac{100}{4}=25\).

Step 2

Why this answer is correct

The correct answer is B. चौड़ाई (25) मीटर / Breadth (25) m. If breadth is (x), length is (100-2x) and area is (A=x(100-2x)). For maximum area, \(x=\frac{100}{4}=25\).

Step 3

Exam Tip

यदि चौड़ाई (x) है तो लंबाई (100-2x) और क्षेत्रफल (A=x(100-2x)) है। अधिकतम के लिए \(x=\frac{100}{4}=25\) है।

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Question 35/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक नाव (24) किमी धारा के अनुकूल और (16) किमी धारा के प्रतिकूल (4) घंटे में जाती है। शांत जल में नाव की चाल (10) किमी प्रति घंटा है। धारा की चाल कितनी है?

A boat covers (24) km downstream and (16) km upstream in (4) hours. Its speed in still water is (10) km per hour. What is the speed of the current?

Explanation opens after your attempt
Correct Answer

B. (2) किमी प्रति घंटा(2) km per hour

Step 1

Concept

Let the current speed be (x). Then \(\frac{24}{10+x}+\frac{16}{10-x}=4\). This gives \(4x^2+8x-16=0\), so (x=2).

Step 2

Why this answer is correct

The correct answer is B. (2) किमी प्रति घंटा / (2) km per hour. Let the current speed be (x). Then \(\frac{24}{10+x}+\frac{16}{10-x}=4\). This gives \(4x^2+8x-16=0\), so (x=2).

Step 3

Exam Tip

धारा की चाल (x) हो तो \(\frac{24}{10+x}+\frac{16}{10-x}=4\)। इससे \(4x^2+8x-16=0\) और (x=2) मिलता है।

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Question 36/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक नाव (30) किमी धारा के अनुकूल और (20) किमी धारा के प्रतिकूल कुल (5) घंटे में जाती है। शांत जल में नाव की चाल (12) किमी प्रति घंटा है। धारा की चाल क्या है?

A boat goes (30) km downstream and (20) km upstream in (5) hours. The speed of the boat in still water is (12) km per hour. What is the speed of the current?

Explanation opens after your attempt
Correct Answer

A. (2) किमी प्रति घंटा(2) km per hour

Step 1

Concept

Let the current speed be (x). Then \(\frac{30}{12+x}+\frac{20}{12-x}=5\). Solving gives \(5x^2+10x-60=0\), so (x=2).

Step 2

Why this answer is correct

The correct answer is A. (2) किमी प्रति घंटा / (2) km per hour. Let the current speed be (x). Then \(\frac{30}{12+x}+\frac{20}{12-x}=5\). Solving gives \(5x^2+10x-60=0\), so (x=2).

Step 3

Exam Tip

धारा की चाल (x) हो तो \(\frac{30}{12+x}+\frac{20}{12-x}=5\)। हल करने पर \(5x^2+10x-60=0\) और (x=2) मिलता है।

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Question 37/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक बस (300) किमी जाती है। यदि चाल (10) किमी प्रति घंटा कम होती तो (1) घंटा अधिक लगता। वास्तविक चाल क्या है?

A bus travels (300) km. If its speed were (10) km per hour less, it would take (1) hour more. What is the actual speed?

Explanation opens after your attempt
Correct Answer

B. (60) किमी प्रति घंटा(60) km per hour

Step 1

Concept

Let the speed be (x). Then \(\frac{300}{x-10}-\frac{300}{x}=1\). This gives \(x^2-10x-3000=0\), so (x=60).

Step 2

Why this answer is correct

The correct answer is B. (60) किमी प्रति घंटा / (60) km per hour. Let the speed be (x). Then \(\frac{300}{x-10}-\frac{300}{x}=1\). This gives \(x^2-10x-3000=0\), so (x=60).

Step 3

Exam Tip

चाल (x) हो तो \(\frac{300}{x-10}-\frac{300}{x}=1\)। इससे \(x^2-10x-3000=0\) और (x=60) मिलता है।

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Question 38/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक ट्रेन (360) किमी की दूरी तय करती है। यदि उसकी चाल (5) किमी प्रति घंटा अधिक होती तो समय (1) घंटा कम लगता। मूल चाल क्या थी?

A train covers (360) km. If its speed were (5) km per hour more, it would take (1) hour less. What was the original speed?

Explanation opens after your attempt
Correct Answer

A. (40) किमी प्रति घंटा(40) km per hour

Step 1

Concept

Let the speed be (x). Then \(\frac{360}{x}-\frac{360}{x+5}=1\). This gives \(x^2+5x-1800=0\), so (x=40).

Step 2

Why this answer is correct

The correct answer is A. (40) किमी प्रति घंटा / (40) km per hour. Let the speed be (x). Then \(\frac{360}{x}-\frac{360}{x+5}=1\). This gives \(x^2+5x-1800=0\), so (x=40).

Step 3

Exam Tip

चाल (x) हो तो \(\frac{360}{x}-\frac{360}{x+5}=1\)। इससे \(x^2+5x-1800=0\) और (x=40) मिलता है।

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Question 39/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक भिन्न का हर अंश से (3) अधिक है। यदि भिन्न और उसके व्युत्क्रम का योग \(\frac{29}{10}\) है तो अंश क्या है?

The denominator of a fraction is (3) more than its numerator. If the sum of the fraction and its reciprocal is \(\frac{29}{10}\), what is the numerator?

Explanation opens after your attempt
Correct Answer

A. (2)

Step 1

Concept

The fraction is \(\frac{x}{x+3}\). From \(\frac{x}{x+3}+\frac{x+3}{x}=\frac{29}{10}\), (x=2) or (x=15), and among the options (2) is correct.

Step 2

Why this answer is correct

The correct answer is A. (2). The fraction is \(\frac{x}{x+3}\). From \(\frac{x}{x+3}+\frac{x+3}{x}=\frac{29}{10}\), (x=2) or (x=15), and among the options (2) is correct.

Step 3

Exam Tip

भिन्न \(\frac{x}{x+3}\) है। \(\frac{x}{x+3}+\frac{x+3}{x}=\frac{29}{10}\) से (x=2) या (x=15) आता है और विकल्पों में (2) सही है।

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Question 40/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक भिन्न का हर अंश से (4) अधिक है। यदि अंश और हर दोनों में (2) जोड़ने पर भिन्न \(\frac{3}{5}\) हो जाती है तो मूल अंश क्या है?

The denominator of a fraction is (4) more than its numerator. If (2) is added to both numerator and denominator, the fraction becomes \(\frac{3}{5}\). What is the original numerator?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

The numerator is (x) and denominator is (x+4). From \(\frac{x+2}{x+6}=\frac{3}{5}\), (x=4).

Step 2

Why this answer is correct

The correct answer is A. (4). The numerator is (x) and denominator is (x+4). From \(\frac{x+2}{x+6}=\frac{3}{5}\), (x=4).

Step 3

Exam Tip

अंश (x) और हर (x+4) है। \(\frac{x+2}{x+6}=\frac{3}{5}\) से (x=4) मिलता है।

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Question 41/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के वर्ग से उस संख्या का (14) गुना घटाने पर (51) मिलता है। बड़ी धनात्मक संख्या क्या है?

When (14) times a number is subtracted from its square, the result is (51). What is the larger positive number?

Explanation opens after your attempt
Correct Answer

B. (17)

Step 1

Concept

The equation is \(x^2-14x=51\). From \(x^2-14x-51=0\), (x=17) or (x=-3), so the positive number is (17).

Step 2

Why this answer is correct

The correct answer is B. (17). The equation is \(x^2-14x=51\). From \(x^2-14x-51=0\), (x=17) or (x=-3), so the positive number is (17).

Step 3

Exam Tip

समीकरण \(x^2-14x=51\) है। \(x^2-14x-51=0\) से (x=17) या (x=-3) मिलता है इसलिए धनात्मक संख्या (17) है।

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Question 42/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के वर्ग में उस संख्या का (9) गुना जोड़ने पर (400) मिलता है। धनात्मक संख्या क्या है?

When (9) times a number is added to its square, the result is (400). What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (16)

Step 1

Concept

The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).

Step 2

Why this answer is correct

The correct answer is A. (16). The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).

Step 3

Exam Tip

समीकरण \(x^2+9x=400\) है। \(x^2+9x-400=0\) से धनात्मक हल (x=16) है।

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Question 43/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

किस धनात्मक संख्या में (7) जोड़ने पर प्राप्त संख्या और मूल संख्या का गुणनफल (330) होता है?

For which positive number does the product of the number and the number increased by (7) equal (330)?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).

Step 2

Why this answer is correct

The correct answer is B. (15). Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).

Step 3

Exam Tip

संख्या (x) हो तो (x(x+7)=330)। \(x^2+7x-330=0\) से धनात्मक हल (x=15) है।

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Question 44/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत विषम धनात्मक पूर्णांकों का गुणनफल (483) है। बड़ी संख्या क्या है?

The product of two consecutive positive odd integers is (483). What is the larger integer?

Explanation opens after your attempt
Correct Answer

B. (23)

Step 1

Concept

The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).

Step 2

Why this answer is correct

The correct answer is B. (23). The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) हैं। (x(x+2)=483) से (x=21) मिलता है इसलिए बड़ी संख्या (23) है।

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Question 45/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत सम धनात्मक पूर्णांकों का गुणनफल (360) है। छोटी संख्या क्या है?

The product of two consecutive positive even integers is (360). What is the smaller integer?

Explanation opens after your attempt
Correct Answer

B. (18)

Step 1

Concept

Let the integers be (x) and (x+2). From (x(x+2)=360), \(x^2+2x-360=0\), so (x=18).

Step 2

Why this answer is correct

The correct answer is B. (18). Let the integers be (x) and (x+2). From (x(x+2)=360), \(x^2+2x-360=0\), so (x=18).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) मानें। (x(x+2)=360) से \(x^2+2x-360=0\) और (x=18) मिलता है।

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Question 46/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक वर्गाकार मैदान की भुजा (4) मीटर बढ़ाने पर क्षेत्रफल (96) वर्ग मीटर बढ़ जाता है। मूल भुजा कितनी थी?

When the side of a square field is increased by (4) m, its area increases by (96) square m. What was the original side?

Explanation opens after your attempt
Correct Answer

B. (10) मीटर(10) m

Step 1

Concept

If the original side is (x), then ((x+4)2-x-2=96). Thus (8x+16=96), giving (x=10).

Step 2

Why this answer is correct

The correct answer is B. (10) मीटर / (10) m. If the original side is (x), then ((x+4)2-x-2=96). Thus (8x+16=96), giving (x=10).

Step 3

Exam Tip

मूल भुजा (x) हो तो ((x+4)2-x-2=96)। इससे (8x+16=96) और (x=10) मिलता है।

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Question 47/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक आयताकार बगीचे की लंबाई चौड़ाई से (5) मीटर अधिक है। यदि क्षेत्रफल (336) वर्ग मीटर है तो चौड़ाई क्या होगी?

The length of a rectangular garden is (5) m more than its breadth. If its area is (336) square m, what is the breadth?

Explanation opens after your attempt
Correct Answer

B. (16) मीटर(16) m

Step 1

Concept

Taking breadth as (x), we get (x(x+5)=336). From \(x^2+5x-336=0\), (x=16) is correct.

Step 2

Why this answer is correct

The correct answer is B. (16) मीटर / (16) m. Taking breadth as (x), we get (x(x+5)=336). From \(x^2+5x-336=0\), (x=16) is correct.

Step 3

Exam Tip

चौड़ाई (x) लेने पर (x(x+5)=336) बनता है। \(x^2+5x-336=0\) से (x=16) सही है।

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Question 48/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक आयत की लंबाई उसकी चौड़ाई से (3) सेमी अधिक है और क्षेत्रफल (180) वर्ग सेमी है। चौड़ाई कितनी है?

The length of a rectangle is (3) cm more than its breadth and its area is (180) square cm. What is the breadth?

Explanation opens after your attempt
Correct Answer

C. (12) सेमी(12) cm

Step 1

Concept

Let the breadth be (x). From (x(x+3)=180), \(x^2+3x-180=0\) and (x=12).

Step 2

Why this answer is correct

The correct answer is C. (12) सेमी / (12) cm. Let the breadth be (x). From (x(x+3)=180), \(x^2+3x-180=0\) and (x=12).

Step 3

Exam Tip

मान लें चौड़ाई (x) है। (x(x+3)=180) से \(x^2+3x-180=0\) और (x=12) मिलता है।

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Question 49/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक आयत का परिमाप (50) सेमी और क्षेत्रफल (150) वर्ग सेमी है। उसकी लंबाई और चौड़ाई क्या हैं?

A rectangle has perimeter (50) cm and area (150) square cm. What are its length and breadth?

Explanation opens after your attempt
Correct Answer

A. (10) सेमी और (15) सेमी(10) cm and (15) cm

Step 1

Concept

Here (l+b=25) and (lb=150). This gives \(t^2-25t+150=0\), so the measures are (10) cm and (15) cm.

Step 2

Why this answer is correct

The correct answer is A. (10) सेमी और (15) सेमी / (10) cm and (15) cm. Here (l+b=25) and (lb=150). This gives \(t^2-25t+150=0\), so the measures are (10) cm and (15) cm.

Step 3

Exam Tip

(l+b=25) और (lb=150) है। इससे \(t^2-25t+150=0\) बनता है और माप (10) सेमी तथा (15) सेमी हैं।

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Question 50/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो संख्याओं का योग (31) और गुणनफल (234) है। छोटी संख्या क्या है?

The sum of two numbers is (31) and their product is (234). What is the smaller number?

Explanation opens after your attempt
Correct Answer

B. (13)

Step 1

Concept

If one number is (x), the other is (31-x). From (x(31-x)=234), the numbers are (13) and (18).

Step 2

Why this answer is correct

The correct answer is B. (13). If one number is (x), the other is (31-x). From (x(31-x)=234), the numbers are (13) and (18).

Step 3

Exam Tip

यदि एक संख्या (x) है तो दूसरी (31-x) होगी। (x(31-x)=234) से संख्याएँ (13) और (18) मिलती हैं।

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Question 51/1750 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

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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Question 52/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक नाव (30,किमी) धारा के विरुद्ध और (30,किमी) धारा के साथ कुल (8,घंटे) में जाती है। धारा की चाल (2,किमी/घंटा) है। शांत जल में नाव की चाल क्या है?

A boat travels (30,km) upstream and (30,km) downstream in a total of (8,hours). The speed of the stream is (2,km/h). What is the speed of the boat in still water?

Explanation opens after your attempt
Correct Answer

B. \((8,\text{किमी\)घंटा}) / (8,km / h)

Step 1

Concept

If the still-water speed is (x), then \(\frac{30}{x-2}+\frac{30}{x+2}=8\). Solving gives (x=8).

Step 2

Why this answer is correct

The correct answer is B. (8,किमी / घंटा) / (8,km / h\(). If the still-water speed is (x), then (\frac{30}{x-2}+\frac{30}{x+2}=8). Solving gives (x=8).\)

Step 3

Exam Tip

यदि शांत जल की चाल (x) है तो \(\frac{30}{x-2}+\frac{30}{x+2}=8\)। हल करने पर (x=8) मिलता है।

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Question 53/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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?

Explanation opens after your attempt
Correct Answer

B. (12)

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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Question 54/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक आयताकार हाल की लंबाई चौड़ाई से (2,मी) अधिक है और क्षेत्रफल \(168,मी^2\) है। चौड़ाई क्या है?

The length of a rectangular hall is (2,m) more than its breadth and its area is (168,m\(^2). What is the breadth\)?

Explanation opens after your attempt
Correct Answer

C. (12,मी)(12,m)

Step 1

Concept

If breadth is (x), then (x(x+2)=168). The positive solution is (x=12).

Step 2

Why this answer is correct

The correct answer is C. (12,मी) / (12,m\(). If breadth is (x), then (x(x+2)=168). The positive solution is (x=12).\)

Step 3

Exam Tip

यदि चौड़ाई (x) है तो (x(x+2)=168)। धनात्मक हल (x=12) है।

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Question 55/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक द्विअंकीय संख्या में इकाई अंक दहाई अंक से (1) अधिक है। अंकों के वर्गों का योग (41) है। संख्या क्या है?

In a two-digit number, the units digit is (1) more than the tens digit. The sum of the squares of the digits is (41). What is the number?

Explanation opens after your attempt
Correct Answer

B. (45)

Step 1

Concept

If the tens digit is (x), then (x-2+(x+1)2=41). Thus (x=4) and the number is (45).

Step 2

Why this answer is correct

The correct answer is B. (45). If the tens digit is (x), then (x-2+(x+1)2=41). Thus (x=4) and the number is (45).

Step 3

Exam Tip

दहाई अंक (x) हो तो (x-2+(x+1)2=41)। इससे (x=4) और संख्या (45) है।

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Question 56/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक ट्रेन (240,किमी) चलती है। गति (10,किमी/घंटा) बढ़ाने पर समय (2,घंटे) कम हो जाता है। मूल गति क्या थी?

A train travels (240,km). When its speed is increased by (10,km/h), the time decreases by (2,hours). What was the original speed?

Explanation opens after your attempt
Correct Answer

B. \((30,\text{किमी\)घंटा}) / (30,km / h)

Step 1

Concept

If the speed is (x), then \(\frac{240}{x}-\frac{240}{x+10}=2\). Solving gives (x=30).

Step 2

Why this answer is correct

The correct answer is B. (30,किमी / घंटा) / (30,km / h\(). If the speed is (x), then (\frac{240}{x}-\frac{240}{x+10}=2). Solving gives (x=30).\)

Step 3

Exam Tip

यदि गति (x) है तो \(\frac{240}{x}-\frac{240}{x+10}=2\)। हल करने पर (x=30) मिलता है।

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Question 57/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत धनात्मक विषम संख्याओं के वर्गों का योग (394) है। छोटी संख्या क्या है?

The sum of the squares of two consecutive positive odd numbers is (394). What is the smaller number?

Explanation opens after your attempt
Correct Answer

B. (13)

Step 1

Concept

If the numbers are (x) and (x+2), then (x-2+(x+2)2=394). This gives (x=13).

Step 2

Why this answer is correct

The correct answer is B. (13). If the numbers are (x) and (x+2), then (x-2+(x+2)2=394). This gives (x=13).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) हों तो (x-2+(x+2)2=394)। इससे (x=13) है।

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Question 58/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक आयताकार पेज का क्षेत्रफल (300,सेमी\(^2) है और लंबाई चौड़ाई से (5\),सेमी) अधिक है। चौड़ाई क्या है?

A rectangular page has area (300,cm\(^2) and its length is (5\),cm) more than its breadth. What is the breadth?

Explanation opens after your attempt
Correct Answer

C. (15,सेमी)(15,cm)

Step 1

Concept

If breadth is (x), then (x(x+5)=300). This gives (x=15).

Step 2

Why this answer is correct

The correct answer is C. (15,सेमी) / (15,cm\(). If breadth is (x), then (x(x+5)=300). This gives (x=15).\)

Step 3

Exam Tip

यदि चौड़ाई (x) है तो (x(x+5)=300)। इससे (x=15) मिलता है।

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Question 59/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

(18,मी) लंबी और (12,मी) चौड़ी आयताकार क्यारी के बाहर चारों ओर समान चौड़ाई का रास्ता है। कुल क्षेत्रफल \(352,मी^2\) हो जाता है। रास्ते की चौड़ाई क्या है?

A uniform path is made outside a rectangular bed of length (18,m) and breadth (12,m). The total area becomes (352,m\(^2). What is the width of the path\)?

Explanation opens after your attempt
Correct Answer

B. (2,मी)(2,m)

Step 1

Concept

If the width is (x), then ((18+2x)(12+2x)=352). The practical solution is (x=2).

Step 2

Why this answer is correct

The correct answer is B. (2,मी) / (2,m\(). If the width is (x), then ((18+2x)(12+2x)=352). The practical solution is (x=2).\)

Step 3

Exam Tip

यदि चौड़ाई (x) है तो ((18+2x)(12+2x)=352)। इससे व्यावहारिक हल (x=2) मिलता है।

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Question 60/1750 Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

(40,मी) तार से एक आयत बनाया गया जिसका क्षेत्रफल \(96,मी^2\) है। लंबाई और चौड़ाई का अंतर क्या है?

A rectangle is made from (40,m) of wire and its area is (96,m\(^2). What is the difference between its length and breadth\)?

Explanation opens after your attempt
Correct Answer

B. (4,मी)(4,m)

Step 1

Concept

Here (l+b=20) and (lb=96). The dimensions are (8) and (12), so the difference is (4).

Step 2

Why this answer is correct

The correct answer is B. (4,मी) / (4,m\(). Here (l+b=20) and (lb=96). The dimensions are (8) and (12), so the difference is (4).\)

Step 3

Exam Tip

यहाँ (l+b=20) और (lb=96) है। आयाम (8) और (12) हैं इसलिए अंतर (4) है।

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