Two friends, Alex and Bob, go to a bookshop, together with their sons Peter and Tim. All four of them buy some books. Each book costs a whole amount of shillings.

When they leave the shop, they notice that both fathers have spent 21 shillings more than their respective sons. Moreover, each of them paid per book the same amount of shillings as the number of books that he bought.

The difference between the number of books that Alex bought and that Peter bought is five.

Who is the father of Tim?

Sorry about the last. I hit enter instead of tab after typing the title.

Consider the statement that "Moreover, each of them paid per book the same amount of shillings as the number of books that he bought." This means that, for example, if Tim bought one book, it cost one shlling, and if Peter bought two books, they averaged 2 shillings, so his bill was 4 shillings. In General, a person's bill is the square of the number of books he bought.

If Peter bought "p" books, then Alex bought (p +/- 5) books. Alex' bill is (p + 5)^2 = p^2 +/- 10p + 25.

Assuming that there is a legitimate solution to the problem, since 25 + 10p =21 means that 10p= -4; and 25 - 10p = 21 means that 10p = 4 neither of which allows a whole number solution for p, Peter is not Alex' son, so Tim must be.

Posted by TomM on 2002-05-16 16:20:01