Mathematics
Word Problems and Applications
Practice questions
A rectangle is made using a 40 m long wire. If its area is 96 square metres, what is the difference between its length and breadth?A uniform path is constructed all around the outside of a rectangular bed that is 18 metres long and 12 metres wide. The total area of the bed and the path is 352 square metres. What is the width of the path?A rectangular page has an area of \(300\,\text{cm}^2\), and its length is \(5\,\text{cm}\) more than its breadth. What is the breadth of the page?The sum of the squares of two consecutive positive odd numbers is \(394\). Find the smaller number.A train travels a distance of 240 km. If its speed is increased by 10 km/h, the travel time decreases by 2 hours. What was the train's original speed?In a two-digit number, the units digit is 1 more than the tens digit. The sum of the squares of the two digits is 41. What is the number?The length of a rectangular hall is 2 metres more than its breadth. If the area of the hall is 168 square metres, what is its breadth?Some students donated money. Each student donated 2 rupees more than the total number of students, and the total amount collected was 168 rupees. How many students were there?A boat travels (30,\text{km}) upstream and (30,\text{km}) downstream in a total of (8,\text{hours}). The speed of the stream is (2,\text{km/h}). What is the speed of the boat in still water?The product of two consecutive positive integers is 552. Which two integers are they?The sum of two numbers is (31) and their product is (234). What is the smaller number?A rectangle has perimeter (50) cm and area (150) square cm. What are its length and breadth?The length of a rectangle is 3 cm more than its breadth, and its area is 180 square cm. What is the breadth of the rectangle?The length of a rectangular garden is 5 m more than its breadth. If the area of the garden is 336 square metres, what is its breadth?When the side of a square field is increased by 4 m, its area increases by 96 m². What was the original side length?The product of two consecutive positive even integers is 360. What is the smaller integer?The product of two consecutive positive odd integers is 483. Find the larger integer.Which positive number has a product of 330 with the number obtained by adding 7 to it?When 9 times a number is added to the square of the number, the result is 400. What is the positive number?When (14) times a number is subtracted from its square, the result is (51). What is the larger positive number?