Bank Cashier Mistake Puzzle

Bank Cashier Mistake

You went to a bank to cash out your cheque.
By mistake the bank cashier gives you-
  • Dollar amount in cent, and
  • Cent amount in dollars.
On the way home you spends 5 cent, and then suddenly you notices that you have twice the amount of your cheque.
How much was have you written on 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,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

You went to a bank to cash out your cheque. By mistake the bank cashier gives you- Dollar amount in cent, and Cent amount in dollars. On the way home you spends 5 cent, and then suddenly you notices that you have twice the amount of your cheque.