Linear Equations test paper for class 10

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CBSE TEST PAPER 10th
Linear Equations

1. If twice the son’s age in years is added to the age of his father the sum is 90. If twice the father’s age in year is added to the age of the son, the sun in 120. Find their ages.

2. Ram is three times as old as Rahim. Five years later, Ram will be two-and-a –half times as old as Rahim. How old are Ram and Rahim now?

3. If the numerator of a fraction is multiplied by 2 and its denominator is increased by 2, it becomes 6/7. If instead we multiply the denominator by 2 and increase the numerator by 2 it reduces to 1/2. What is the fraction?

4. A fraction becomes 4/5 if 1 is added to each of the numerator and the denominator. However,
if we subtract 5 from each, the fraction becomes 1/2 find the fraction.

5. If we add 1 in the numerator of a fraction and subtract 1 from its denominator, the fraction becomes 1, It is also given that the fraction becomes 1/2 when we add 1 to its denominator, and then what is the fraction.

6. If we add 5 to the denominator and subtract 5 from the numerator of fraction, it reduces to 1/7 if we subtract 3 from the numerator and add 3 to its denominator it reduces to 1/3. Find the fraction.

7. The denominator of a fraction is 4 more than twice the numerator. When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Determine the fraction.

8. The sum of the numerator and denominator of a fraction is 4 more than twice the numerator if the numerator and denominator are increased by 3, they are is the ratio 2 : 3. Determine the fraction.

9. Two audio cassettes and three video cassettes cost Rs. 340. but three audio cassettes and two video cassettes cost Rs 260. Find the price of an audio cassettes and that of a video cassettes.

10. Mala purchased 5 chairs and 2 tables for Rs. 1625. Reshma purchased 2 chairs and 1 table for Rs. 750. Find the cost per chair and per table.

11. If we buy 2 tickets from station A to station B, and 3 tickets from station A to station C, we have to pay Rs 795. but 3 ticket from station A to B and 5 ticket from station A to C cost a total of Rs 1300. What is the fare from station A to B and that from station A to C?

12. Aman travels 370 km partly by train and partly by car if he covers 250 km by train and the rest by car, it takes him 4 hours but if he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.

13. The area of a rectangle get reduced by 9 square unit, if its length is reduced by 5 unit and the breadth is increased by 3unit if we increase the length by 3 unit and the breadth by 2 units, then the area is increased by 67 square unit. Find the length and the breadth of the rectangle.

14. If in a rectangle, the length is increased and the breadth is reduced by 2 units each, the area is reduced by 28 square units. If the length is reduced by 1 unit, and breadth increased by 2 units, the area increases by 33 square units. Find the dimensions of the rectangle.

15. The area of a rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and the breadth in increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area in creased by 50 square units. Find the length and breadth of the rectangle.

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