A women walks into a bank to cash out her check.

By mistake the bank teller gives her rupee amount in change, and her paise amount in rupees.

On the way home she spends 5 paise, and then suddenly she notices that she has twice the amount of her check.

How much was her check amount ?

The check was for Rupees 31.63.

The bank teller gave her Rupees 63.31

She spent .05, and then she had Rupees 63.26, which is twice the check.

Let x be the rupees of the check, and y be the paise.

The check was for 100x + y paise

He was given 100y + x paise

Also

100y + x - 5 = 2(100x + y)

Expanding this out and rearranging, we find:

98y = 199x + 5

or 199x ≡ -5 (mod 98)

or 98*2*x + 3x ≡ -5 (mod 98)

3x ≡ -5 ≡ 93 (mod 98)

this quickly leads to x = 31