Bananas and Pears

A man bought nine bananas and six pears. He could not recall the prices, but remembered that each banana cost one penny more than each pear, and that the whole sum he paid for the pears was the figure he paid for the bananas with its two digits reversed. He paid less than a pound, that is under a hundred pence, for each kind. How much did he pay altogether?

Solution

Let a pear cost $p$ pence, so a banana costs $p + 1$. The bananas came to $9(p + 1)$ pence and the pears to $6p$ pence, and we are told the pear figure is the banana figure reversed, with both under $100$.

Testing the few pear prices that keep both totals to two digits, $p = 6$ works and nothing else does: the bananas cost $9 \times 7 = 63$ pence and the pears $6 \times 6 = 36$ pence, and $36$ is indeed $63$ written backwards. So altogether he paid $$63 + 36 = 99 \text{ pence,}$$ a penny short of a pound.