Question

A certain number of two-rupee coins and a certain number of five-rupee coins in a piggy bank of a child amount to ₹47. If the number of each kind are interchanged, they would amount to ₹3 less than before. Find the number of coins of each kind.

Answer 1

Here, let the number of ₹ 2 coins be x,

And the number of ₹ 5 coins is y.

According to the given conditions:

(i) The total value is ₹ 47:

2x + 5y = 47     ...(1)

(ii) If the numbers of each kind are interchanged:

₹ 2 coins become y, and ₹ 5 coins become x,

So, the value becomes:

2y + 5x

This is ₹ 3 less than 47, i.e., ₹ 44:

5x + 2y = 44     ...(2)

Now, solving equations:

Multiplying equation (1) by 5:

5(2x + 5y) = 5(47)

10x + 25y = 235     ...(3)

Multiplying equation (2) by 2:

2(5x + 2y) = 2(44)

10x + 4y = 88     ...(4)

Subtracting equation (4) from equation (3):

(10x + 25y) − (10x + 4y) = 235 − 88

10x + 25y − 10x − 4y = 147

10x − 10x + 25y − 4y = 147

21y = 147

y = `147/21`

∴ y = 7

Substitute y = 7 in equation (1):

2x + 5(7) = 47

2x + 35 = 47

2x = 47 − 35

2x = 12

x = `12/2`

∴ x = 6

Hence, the child has 6 coins of ₹ 2 and 7 coins of ₹ 5.