CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set A

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