In how many ways can Rs. 18.75 be paid in exactly 85 coins consisting of 50-paisa, 25-paisa and 10-paisa coins?

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Solution

The correct option is D
8

Suppose we take x = 50-paisa coins, y = 25-paisa coins and z =10-paisa coins.

We have x + y + z = 85 and 50x + 25y + 10z = 1875, because x, y and z are all integers, z should be a multiple of 5.

Possible values are
$\begin{matrix} x & y & z 2 & 63 & 20 5 & 55 & 25 8 & 47 & 30 . . . . . . . . 23 & 7 & 55 \end{matrix}$

So there are eight solutions.

You should notice here that an increase of 5 in z and 3 in x and decrease of 8 in y neither changes the number of coins nor the value.

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