Bank Cashier Mistake

March 21, 2023

Mistake of Bank Cashier Puzzle

You went to a bank to cash out your cheque. By mistake the bank cashier gives you-

The dollar amount in cents, and
Cent amount in dollars.

On the way home, you spend 5 cents, and then suddenly you notice that you have twice the amount of your cheque.

How much have you written on the cheque ?

Solution

Method : Lets assume Cent = z and $ = 100z , no. of dollars =x and no.of cents = y

So,Initially he had 100zx + zy

Now after cashier’s mistake it becomes 100zy + zx

After spending 5 cents it becomes double

So now equation is 100zy + zx -5z = 200zx + 2zy

or 199x = 98y -5

Now, the value of y cannot be greater than 100 (otherwise it becomes $)

so plotting values of y for 1 to 100,we get only 1 integer value for x i.e. 31 for y = 63

Hence the answer 31$ and 63 cents

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