Mathematics
Word Problems and Applications
Practice questions
A number exceeds its reciprocal by (\frac{15}{4}). What is the positive number?The sum of a number and its reciprocal is (\frac{17}{4}). What is the larger value of the number?The diagonal of a rectangle is 25 cm, and its length is 17 cm more than its breadth. What is the breadth of the rectangle?Let the length of a rectangle be \(x\) metres. If its diagonal is 37 metres and its breadth is 12 metres, which quadratic equation can be formed to find \(x\)?The area of a right triangle is 84 square cm, and one perpendicular side is 5 cm longer than the other. What is the length of the shorter perpendicular side?The outer radius of a circular path is 3 m greater than its inner radius. If the area of the path is 75π square metres, what is the inner radius?A square tile has side \(x\) cm. When a 5 cm wide border is added around it, the total area of the outer square becomes 900 square cm. What is the original side of the tile?A rectangular photo has length (8) cm more than its breadth. A (2) cm wide frame is added all around and the total area is (480) square cm. What is the breadth of the photo?A class had to collect a fixed total amount through equal contributions from 30 students. When 5 students were absent, each present student had to pay 20 rupees more than the originally determined contribution. What was the total amount collected?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?A work is completed in (x) days. If (2) workers are added, the same work is completed (3) days earlier. If total work is (60) worker-days, how many workers were there initially?One pipe fills a tank (5) hours faster than another pipe. Together they fill the tank in (6) hours. In how many hours will the faster pipe alone fill it?Two pipes fill a tank individually in \(x\) hours and \(x+6\) hours, respectively. Together, they fill the tank in 4 hours. How long does the faster pipe take to fill the tank alone?A shopkeeper bought x items for 720 rupees. If he had received 3 more items for the same total amount, the cost per item would have been 40 rupees less. What is the value of x?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?The product of the numbers obtained by subtracting 5 from and adding 5 to a number is 119. What is the positive number?The square of a positive number is 60 more than 11 times the number. What is the number?Which of the following situations is generally represented by a quadratic equation?The difference between two positive numbers is 9, and the sum of their squares is 521. What is the smaller number?(240) students are arranged in equal rows. If the number of rows is reduced by (4), each row will have (5) more students. What was the original number of rows?