**Chapter 3 - Linear equation in two variables - Revision Assignment**

Class X Mathematics

1. The sum of two numbers is 6 and their difference is 4. Find the numbers

2. The sum of two numbers is 15. If the sum of their reciprocals is 3/10. Find the numbers

3. The sum of two numbers as well as the difference between their squares is 9. Find the numbers

4. If we add 5 to the denominator and subtract 5 from the numerator of a fraction, it reduces to 1/8. If we subtract 3 from the numerator and add 3 to its denominator, it reduces to 2/7. Find the fraction

5. The numerator and denominator of a fraction are in the ratio 2:3. If 6 is subtracted from the numerator , the fraction becomes two –thirds of its original value. Find fraction

6. If numerator of a fraction is multiplied by 3 and its denominator is increased by 3, it becomes 3⁄4. If instead we multiply the denominator by 3 and increase the numerator by 3 , it reduces to 1/3. What is fraction.

7. Amit is ten years older than Gaurav. Five years ago one seventh of Amit age was equal to one fifth of Gaurav age. Find their present ages.

8. Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages.

9. Vikram’s age is four times the sum of the ages of his two sons. Six years hence , his age will be double the sum of their ages. Find their present age.

10. The sum of the digits of a two digit number is 15. The number obtained by interchange the digit exceeds the given number by 9. Find the number

11. The sum of a two digit number and the number formed by interchange its digit 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.

12. A women has 60 notes in all of ₹ 10 and ₹ 20 denomination. If the total worth of the notes is ₹ 850, find out how many notes of each kind does she have.

13. 800 people collectively paid Rs 67500 for watching a film show occupying the balcony and the rear stall seats. If the charges for the balcony seat and rear stall were Rs 100 and Rs 75 respectively, how many more audience occupied the rear stall seats?

14. A man travel 370 km, partly by train and partly by car. If he covers 250 km by train and the rest by car , it take him 4 hours. But if he travel 130 km by train and the rest by car, it takes 18 minutes longer. Find the speed of the train and that of car.

15. A and B are cycling along the circular boundary of a playground. If they start towards each other from the opposite ends of the diameter 150 m long with A riding at twice the speed of B, then find the distance (in term of π) travelled by B when the two meet.

16. There are two examination rooms A and B. if 10 candidates are sent from A to B, the number of students in each room is the same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. find the number of students in each room.

17. A person can row 4 km upstream and 16 km downstream in 1 hour 50 minutes. He can row 20 km downstream and 20 km upstream in 4 hours 10 minutes. Find the speed of the person in still water and the speed of the current.

18. A train covers a certain distance at a uniform rate. On increasing its speed by 5 km/h it saves 20 minutes and on decreasing its speed by 20 km/h it loses 2 hours. Find the distance covered by train.

19. A man sold a chair and a table together for ₹ 1520 there by making a profit of 25 % on the chair and 10% on the table. By selling them together for ₹ 1535, he would have made a profit of Rs 10% on the chair and 25% on the table. Find the cost price of each.

20. A salt solution containing 60% salt and another salt solution containing 30% salt are mixed so as to get 20 litres of a 45% salt solution. Find how many litres of each type of solution should be mixed so as to achieve the desired result.

21. A cyclist after riding a certain distance stopped for half an hour to repair his bicycle after which he completed the whole journey of 30 km at half the speed in 5 hours. If the break down had occurred 10 km further off , he would have done the whole journey in 4 hours. Find where the break down occurred and his original speed (ignore bicycle repair time).

22. In an examination one mark is awarded for each correct answer while 1⁄2 marks is deducted for every wrong answer. Jaya answered 120 questions and got 90 marks. How many questions did she answer correctly?

23. A person rowing at the rate of 5 km/h in still water , takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

24. A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs ₹ 2530. Also one reserved first class ticket and one reserved first class half ticket from A to B costs ₹ 3810. Find the full fare and reservation charge.

25. Vijay had some bananas ,and he divided them into two lots A and B. He sold the first lot at the rate of ₹ 2 for 3 bananas and the second lot at the rate of ₹ 1 per banana, got a total of ₹ 400.if he had sold the first lot at the rate of ₹ 1 per bananas and the second lot at the rate of ₹ 4 for 5 bananas , got a total of ₹ 460.Find the total number of bananas he had.

26. It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. How long would it take for each pipe to fill the pool separately?

27. Graphically, solve the equations

*2x+y =6*and

*2x-y =-2*and find the ratio of the areas of the two triangles formed by these lines with the x-axis and the lines with the y axis.

28. Determine, graphically, the vertices of the triangle formed by the lines ,

(i)

*y=x , 3y=x , x+y =8*

(ii)

*3x-y =3 ,2x-3y =2, x+2y-8*

29. Draw the graphs of the equations x=3, x=5 and 2x-y-4 =0. Also find the area of the quadrilateral formed by the lines and the x axis.

30. Solve the equations

*21x +47y = 110 ,*

*47x+ 21y = 162*

31. Find the value of unknown when equation has infinite many solutions.

(i)

*x+(k+1)y =4 , (k+1)x +9y = 5k +2*

(ii)

*(k-1) x –y =5 , (k+1)x + (1-k)y = 3k+1*

(iii)

*2x-y =5 , (p+q)x + (2q-p)y = 15*

32. Find the value of unknown when equation has no solutions

(i)

*(3k+1)x +3y-2 =0 , (k 2 +1)x +(k-2)y -5=0*

(ii)

*3x +y =1 , (2k-1) x + (k-1)y –(2k+1) =0*

33. Find the value of unknown when equation has unique solution

(i)

*9x +py-1 =0, 3x+4y-2 =0*

(ii)

*2x-3y=1 , kx+5y=7*

Answers:

1. 5,1

2. 5,10

3. 5,4

4. 7/11

5. 18/27

6. 2/5

7. Amit = 40, Gaurav = 30

8. Father = 42 years, son = 10 years

9. Vikram = 36, son = 9

10. 78

11. 64

12. 35,25

13. 200

14. 100 km/h, 80 km/h

15. 25π

16. 100 ,80

17. 10 ,8

18. 350 km

19. chair = ₹600, Table = ₹700

20. 10

21. 10 km, 10 km/h

22. 100

23. 2.5 km/h

24. 2500, 30

25. 500

26. 20 h ,30 h

27. 4:1

28. (i) (0,0) (4,4) (6,2)

(ii) (1,0)(2,3)(4,2)

29. 8 sq units

30. x=3, y=1

31. (i) 2 (ii) 3 (iii) p=5 ,q=1

32. (i) -1 (ii) 2

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