CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set A

Question. Which of the following is true if following pair of linear equations has unique solution?
3x – 2y = – 8
(2m – 5)x + 7y – 6 = 0
(a) m = 11/4
(b) m = – 11/4
(c) m ≠ – 11/4
(d) m ≠ 11/4

Answer : C

Question. The perimeter of a rectangle is 40 cm. The ratio of its sides is 2 : 3. Find its length and breadth.
(a) l = 10 cm, b = 8 cm
(b) l = 12 cm, b = 8 cm
(c) l = 12 m, b = 8 m
(d) l = 40 m, b = 30 m

Answer : B

Question. Which of the following is the other name for a pair of linear equations in two variables?
(a) Consistent equations
(b) Simultaneous equations
(c) Inconsistent equations
(d) Dependent equations

Answer : B

Question. For which value of p, will the lines represented by the following pair of linear equations be parallel
3x – y – 5 = 0
6x – 2y – p = 0
(a) all real values except 10
(b) 10
(c) 5/2
(d) 1/2

Answer : A

Question. For what values of k will the following pair of linear equations have infinitely many solutions? 
kx + 3y – (k – 3) = 0
12x + ky – k = 0
(a) k = 4
(b) k = 3
(c) k = 6
(d) k = 2

Answer : C

Question. The difference between two numbers is 26 and one number is three times the other. Find them.
(a) 39, 13
(b) 41, 67
(c) 96, 70
(d) 52, 26

Answer : A

Question. Sanjay starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was ₹ 4500 after four years of service and ₹ 5400 after 10 years, find his initial salary and annual increment.
(a) 4000, 200
(b) 3900, 150
(c) 4500, 100
(d) 3800, 250

Answer : B

Question. The pair of linear equations x + 2y = 5 and 3x + 12y = 10 has
(a) unique solution
(b) no solution
(c) more than two solutions
(d) infinitely many solutions

Answer : A

Question. ₹ 49 was divided among 150 children. Each girl got 50 paise and each boy got 25 paise. How many boys were there?
(a) 100
(b) 102
(c) 104
(d) 105

Answer : C

Question. A can do a piece of work in 24 days. If B is 60% more efficient than A, then the number of days required by B to do the twice as large as the earlier work is
(a) 24
(b) 36
(c) 15
(d) 30

Answer : D

Question. X’s salary is half that of Y’s. If X got a 50% rise in his salary and Y got 25% rise in his salary, then the percentage increase in combined salaries of both is
(a) 30
(b) 33(1/3)
(c) 37(1/2)
(d) 75

Answer : B

Question. The points (7, 2) and (–1, 0) lie on a line
(a) 7y = 3x – 7
(b) 4y = x + 1
(c) y = 7x + 7
(d) x = 4y + 1

Answer : B

Question. If the sum of the ages (in years) of a father and his son is 65 and twice the difference of their ages (in years) is 50, what is the age of the father?
(a) 45 years
(b) 40 years
(c) 50 years
(d) 55 years

Answer : A

Question. The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is
(a) −14/3
(b) 2/5
(c) 5
(d) 10

Answer : D

Question. At present ages of a father and his son are in the ratio 7 : 3, and they will be in the ratio 2 : 1 after 10 years. Then the present age of father (in years) is
(a) 42
(b) 56
(c) 70
(d) 77

Answer : C

Question. A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is
(a) 2
(b) 3
(c) 5
(d) 15

Answer : D

Question. x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x + y is
(a) 10
(b) 11
(c) 12
(d) 13

Answer : B

Question. If 3x + 4y : x + 2y = 9 : 4, then 3x + 5y : 3x – y is equal to
(a) 4 : 1
(b) 1 : 4
(c) 7 : 1
(d) 1 : 7

Answer : C

Question. In a number of two digits, unit’s digit is twice the tens digit. If 36 be added to the number, the digits are reversed. The number is
(a) 36
(b) 63
(c) 48
(d) 84

Answer : C

Question. A motor boat takes 2 hours to travel a distance 9 km down the current and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/hour) respectively are
(a) 3, 1.5
(b) 3, 2
(c) 3.5, 2.5
(d) 3, 1

Answer : A

Question. The 2 digit number which becomes (5/6)th of itself when its digits are reversed. The difference in the digits of the number being 1, then the two digits number is
(a) 45
(b) 54
(c) 36
(d) None of these

Answer : B

Question. A man can row a boat in still water at the rate of 6 km per hour. If the stream flows at the rate of 2 km/hr, he takes half the time going downstream than going upstream the same distance. His average speed for upstream and down stream trip is
(a) 6 km/hr
(b) 16/3 km/hr
(c) Insufficient data to arrive at the answer
(d) none of the above

Answer : B

Question. A boat travels with a speed of 15 km/hr in still water. In a river flowing at 5 km/hr, the boat travels some distance downstream and then returns. The ratio of average speed to the speed in still water is
(a) 8 : 3
(b) 3 : 8
(c) 8 : 9
(d) 9 : 8

Answer : C

Question. x and y are two non-negative numbers such that 2x + y = 10. The sum of the maximum and minimum values of (x + y) is
(a) 6
(b) 9
(c) 10
(d) 15

Answer : D

Question. In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is 2 : 3. If further 44 girls leave the class, then the ratio of boys to girls is 5: 2. How many more boys should leave the class so that the number of boys equals that of girls?
(a) 16
(b) 24
(c) 30
(d) 36

Answer : B

Question. The equations 1x + 1/y = 15 and 1/x - 1/y = 5 are such thatax = 1 and by = 1. The values of ‘a’ and ‘b’ respectively are
(a) 10, 5
(b) 10, –5
(c) –5, 10
(d) 5, 10

Answer : A

Question. Consider the following two statements:
I. Any pair of consistent linear equations in two variables must have a unique solution.
II. There do not exist two consecutive integers, the sum of whose squares is 365.
Then,
(a) both I and II are true
(b) both I and II are false
(c) I is true and II is false
(d) I is false and II is true

Answer : B

Question. The average incomes of the people in two villages are P and Q respectively. Assume that P ≠ Q. A person moves from the first village to the second village. The new average incomes are P’ and Q’ respectively. Which of the following is not possible?
(a) P’ > P and Q’ > Q
(b) P’ > P and Q’ < Q
(c) P’ = P and Q’ = Q
(d) P’< P and Q’ < Q

Answer : C

Question. The graphs of the equations x – y = 2 and kx + y = 3, where k is a constant, intersect at the point (x, y) in the first quadrant, if and only if k is
(a) equal to –1
(b) greater than –1
(c) less than 3/2
(d) lying between –1 and 3/2

Answer : D

Question. For what value of p, the following pair of linear equations in two variables will have infinitely many solutions ? px + 3y – (p – 3) = 0, 12x + py – p = 0
(a) 6
(b) – 6
(c) 0
(d) 2

Answer : A

Question. In village Madhubani 8 women and 12 girls can paint a large mural in 10 hours. 6 women and 8 girls can paint it in 14 hours. The number of hours taken by 7 women and 14 girls to paint the mural is
(a) 10
(b) 15
(c) 20
(d) 35

Answer : A

Question. A boat takes 3 hours to travel 30 km downstream and takes 5 hours to return to the same spot upstream. Find the speed of the boat in still water. (km/hr)
(a) 10 km/hr
(b) 8 km/hr
(c) 6 km/hr
(d) 5 km/hr

Answer : B

Question. If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively.
(a) 3 and 5
(b) 5 and 3
(c) 3 and 1
(d) – 1 and – 3

Answer : C

Question. I. If x – y = xy = 1 – x – y, then x + y is 5/3
II. The system of equations 3x + 2y = a and 5x + by = 4 has infinitely many solutions for x and y, then a = 4, b = 3
III. If x/a + y/b = 2 and ax – by = a² – b², then x = a, y = b Which is true?
(a) I only
(b) II only
(c) III only
(d) None of these.

Answer : C

Question. I. If 3x – 5y = –1 and x – y = – 1, then x = –2, y = –1
II. 2x + 3y = 9, 3x + 4y = 5 ⇒ x = –21, y = 17
III. 2x/a + y/b = 2, x/a - y/b = 4 ⇒ x = 2a, y = 2b
Which is true?
(a) I
(b) II
(c) III
(d) None of these

Answer : A

Question. The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has
(a) one solutio
(b) two solutions
(c) infinitely many solutions
(d) no solution

Answer : C

Question. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is
(a) 25
(b) 72
(c) 63
(d) 36

Answer : D

Question. The value of c for which the pair of equations cx – y = 2 and 6x + 2y = 3 will have infinitely many solutions is
(a) 3
(b) – 3
(c) – 12
(d) no value

Answer : D

Question. If a pair of linear equations is inconsistent, then the lines will be
(a) parallel
(b) always coincident
(c) intersecting
(d) coincident

Answer : A

Question. For what values of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?
(a) solution of 3k – 9 = 0
(b) solution of 2k – 8 = 0
(c) 2
(d) 3

Answer : C

Case Study Based Questions

I. Rupesh purchased 3 chairs and one table for ₹1600 and his friend purchased 5 chairs and 2 tables for ₹2900. If in both the cases the price of chairs and tables are the same, Rupesh wants to know some answers of his question what are in his mind. Help him to solve his problems.

Question. Using the cost price of one chair as ‘x’ and the cost price of one table as ‘y’, the linear pair of equations of the above statement are as follows
(a) 3x + y = 1600, 5x + 2y = 2900
(b) 3x – y = 1600, 5x – 2y = 2900
(c) 3x + y = 1600, 5x – 2y = 2900
(d) 3x – y = 1600, 5x + 2y = 2900

Answer : A

Question. The linear pair of equations formed above by the given information are
(a) Consistent
(b) Inconsistent
(c) Dependent
(d) Both (a) and (c)

Answer : D

Question. If lines are drawn for the linear pair of equations formed by the above information, they will
(a) intersect at one point
(b) be parallel to each other
(c) be coincident
(d) not exist

Answer : A

Question. The solutions of the linear pair of equations formed by the above information are
(a) ₹300, ₹700
(b) ₹500, ₹600
(c) ₹450, ₹700
(d) ₹200, ₹1100

Answer : A

Question. If Rupesh had purchased 2 chairs and 2 tables the sum of total cost will be
(a) ₹2200
(b) ₹1800
(c) ₹2000
(d) ₹2400

Answer : C

II. Travelling by a car on a highway gives lots of fun and thrills. People drive and enjoy the moment of thrills.

On morning two friends who are living at a distance of 150 km apart decided to meet at another place. So, they drive their cars from point A and point B at the same time and meet after 15 hours on a highway.
In an another incident they decide to meet in a hurry. So, they drive their cars in opposite directions and meet in one hour.

Question. Using the speed of car at A, x km/h and the speed of car at B, y km/h, the pair of linear equations representing the situation is
(a) 15x + 15y = 150, x + y = 150
(b) 15x – 15y = 150, x + y = 150
(c) 15x – 15y = 150, x – y = 150
(d) 15x + 15y = 150, x – y = 150

Answer : B

Question. On comparing the coefficients of the pair of linear equations formed by the above situations, following conditions can arise:
(a) a₁/a₂ ≠ b₁/b₂
(b) a₁/a₂ = b₁/b₂ ≠ c₁/c₂
(c) a₁/a₂ = b₁/b₂ = c₁/c₂
(d) None of the above

Answer : A

Question. The lines drawn on the graph paper for the pair of linear equations formed due to above situations can have one of following possibilities.
(a) The two lines intersect at one point
(b) The two lines do not intersect
(c) The two lines coincide
(d) Can not be said anything

Answer : C

Question. The solutions of the pair of linear equations formed by above situation is
(a) a unique solution
(b) no solution
(c) infinitely many solution
(d) not to be determined

Answer : A

Question. The speeds of car at A and car at B are
(a) 70 km/h, 80 km/h
(b) 90 km/h, 60 km/h
(c) 80 km/h, 70 km/h
(d) 60 km/h, 90 km/h

Answer : C

Linear Equation In Two Variables

Please click on below link to download CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set A