After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?

Let the sum of ages of 5 members three years ago be S. Their average age then was S/5. Three years later, each of the 4 remaining members aged 3 years, so their total increased by 12. The new member's age is such that the new sum equals S. If the replaced member was x years old and the new member is y years old, then S = (sum of 4 members' ages 3 years ago) + x = (sum of 4 members' current ages - 12) + x. Also, S = (sum of 4 members' current ages) + y. Therefore y = x - 15, meaning the new member is 15 years younger than the replaced member.