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Difficulty: MediumPuzzle Details

Last week I received a cheque from my Grandma and I cashed it at the BrainBashers bank.

I had spent £5.02 before I realised the bank had made a mistake.

They had swapped the pounds with the pence.

I now had exactly 3 times the value of the original cheque.

What was the original cheque's value?

Show Hint Show Answer Print Puzzle
[Ref: ZYEK] © Kevin Stone 

Answer: £10.36.

We are told that:

   (swapped amount - 5.02) = 3 x original amount

If we call the original amount x.yy, and convert to pence to give 100x + y. The swapped amount is therefore 100y + x. Giving:

   (100y + x) - 502 = 3 x (100x + y)

     100y + x - 502 = 300x + 3y

          97y - 502 = 299x

                  y = 299x + 502
                      ----------
                          97

This is an equation that can be solved in a number of ways, the easiest being trial and error.

Since both x and y have to be whole numbers, we quickly find that x=10 gives y=36. QED.


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