Question of Age

Last winter I was in the United Kingdom. Travelling by train from London to Manchester, I had for company two middle-aged Englishmen who were seated opposite to me. Naturally, they did not speak to me - because we hadn't been introduced. But I couldn't help overhearing their conversation. 'How old is Tracy, I wonder? one asked the other. 'Tracy!' the other replied 'Let me see - eighteen years ago he was three times as old as his son.' 'But now, it appears, he is only twice as old as his son,' said the former. I tried to guess Tracy's age, and his son's age. What do you think my solution was?

If the son is x year old, then the father is 2x year old. Eighteen years ago they were both eighteen years younger. The father was 2x - 18 and the son x - 18. We know that then the father was three times as old as the son: 3(x - 18) = 2x - 18 When we solve this equation, we will find that x =36. The son is 36 and the father 72.