Pair of Linear Equation in Two Variables Test

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Pair of Linear Equation in Two Variables Test - 3

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Question 1
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The cost of 3 pencils boxes and 3 erasers boxes is Rs. 150. Four times the cost of pencil box is 20 more than the cost of eraser box. Find the respective costs of a pencil box and an eraser box.

A
Rs. 14, Rs. 36

B
Rs. 15, Rs. 30

C
Rs. 10, Rs. 15

D
Rs. 21, Rs. 13

Solution

Let x and y be the costs of a pencil box and an eraser box, respectively.
According to the question:

3x + 3y = 150
x + y = 50 ... (i)
Also, 4x - y = 20 ... (ii)

Putting the value of y from (i) in (ii), we get 4x - (50 - x) = 20
4x - 50 + x = 20
5x = 70
x = 14

So, x + y = 50
y = 50 - 14 = 36