Maths Puzzle

[detective]

You cash a cheque at your bank but the cashier mistakenly transposes the pounds and pence when he gives you the money, something you don't spot at the time. You spend �2--34 on the way home and then discover you now have twice the amount of the original cheque. What was its value?

[crofter]

He wanted �20.43, but received �43.20.

After spending �2.34, he was left with �40.86

[crofter]

Method of solution: With X pounds and Y pence, convert into pence.

Then 100Y + X - 234 = 2(100X + Y)

So 98Y = 199X + 234 so Y = (199X + 234)/98

Search through the values of X (evens only) looking for when the value of (199X + 234)/ 98 is a whole number. It happens when X = 20 making Y = 43.

A similar problem occurred last week with Rupees and Piase (or something)