10th Linear equation in one variable

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 restby 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 thebreadth in increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5units, the area in creased by 50 square units. Find the length and breadth of the rectangle.

16. A person starts his job with a certain monthly salary and earns a find increment every year. If his salary was Rs. 4500 after 4 years of service and Rs. 5400 after. 10 years of service, find his initial salary and the annual increment.

17. taxi charges consists of fixed charges and the remaining depending upon the distance traveled 70 km, he pay s Rs. 500 and for traveling 100 km, he pays Rs 680 express the above statements with the help of simultaneous equations and hence find the fixed charges and the rate per km

18. The total expenditure per month of a house hold consists of a fixed rent of the house and the mess charge depending upon the number of people sharing the house. The total monthly expenditure is Rs. 3,900 for 2 people and Rs. 7,500 for 5 people. Find the rent of the house and the mess charges per head per month.

19. A railway half- ticket costs half the full fare but the reservation charges are the same on a halfticket as on a full ticket one reserved first class ticket from station A to station B costs Rs. 2125.Also, one reserved first class ticket and one reserved half first class ticket from A to B cost Rs. 3200. find the full fare from station A to B and also the reservation charges for a ticket.

20. The sum of the digits of a two- digit number is 8. The number obtained by inter changing the two digits exceeds the given number by 36. find the number.

21. The sum of the digits of a two digits number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits of the number. Find the number.

22. Seven times a two digits number is the same as four times the number obtained on

interchanging the digits of the given number. If one digit of the given number exceeds the other by 3, find the number.

23. A two digit number is obtained by either multiplying the sum of the digits by 8 and adding 1, or by multiplying the difference of the digits by 13 and adding 2. Find the number. How many such numbers are there?

24. A two- digits number is 4 times the sum of its digits. If 18 is added to the number, the digits are revered. Find the number.

25. A two- digits number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number the digits are reversed. Find the number.

26. The sum of a two digit number and the number formed by interchanging its digits is 110. if 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. find the first number.

27. The sum of a two digits number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.

28. A number consists of two digits is seven times he sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.

29. A number consists of two digits. When it is divided by the sum of the digits, the quotient is 7. If 27 is subtracted from the number, the digits are reversed. Find the number.

30. A number consists of two digits when it is divided by sum of the digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number.

33. Places A and B are 80 km apart from each other on a highway. A car starts from A and

another from B at the same time . If they moves in the same direction, they meet in 8 hours and ifthey move in opposite directions, they meet in 1 hours and 20 minutes. Find the speed of the cars.

34. Points A and B are 100 km apart on a highway. One car starts from A and another from B atthe same time. If the car travel in the same direction at a constant speed, they meet in 5 hours if the car travel towards each other, they meet in 1 hour. What are the speeds of the two cars.

35. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream is the same time. Find the speed of the boat in still water and the speed of the stream.

36. A boat goes 16 km upstream and 24 km down stream in 6 hours. It can go 12km upstream and 36km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

37. A Person can row 8 km upstream and 24 km down stream in 4 hours. He can row 12 km downstream and 12 km upstream in4 hours. Find the speed of the person in still water and also thespeed of the current.

38. There are two class rooms A and B containing students. If 5 students are shifted from room A to room B, the resulting number of students in the two rooms become equal. If 5 student are shifted from room B to room A, the resulting number of student's in room A becomes double the number of student left in room B. find the original number of student in the two rooms seperately.

39. The coach of a cricket team buys three bats and six balls for Rs. 3900. Later, she buys another bat and two more balls of the same kind for Rs. 1300. Represent this situation algebraically and geometrically(graphically).

[x + 2y = 1300 and x + 3y = 1300, where x = cost in Rs. of one ball and y = cost in Rs. of bat].

40. The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month,the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically(graphically).[2x + y = 160 and 4x + 2y = 300, where x = price of 1 kg (in Rs.) of apple and y = price of 1 kg (inRs. ) of grapes].

41. Akhila went to a fair with Rs. 20 and want to have rides on the Giant Wheel and play Hoopla. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. If each ride costs Rs. 3 and a game of Hoopla costs Rs. 4, how would you find out the number of rides she had and how many times she played Hoopla.[x – 2y = 0 and 3x + 4y = 20 ; the value of x = 4 and y = 2].

42. Romila went to a stationary shop and purchased 2 pencils and 3 erasers for Rs. 9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for Rs. 18. Represent this situation algebraically and graphically. [2x + 3y = 9 and 4x + 6y = 18].

43. Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Represent this situation geometrically.