When one member of a 15-strong walking club is replaced by a new member, the club's average age goes up by 8 months. By how much is the new member older than the one who left?

The club still has 15 members, so a rise of 8 months in the average means the total of the ages rose by $15\times 8=120$ months, which is 10 years. The only change was the swap, so the newcomer is 10 years older than the member who left. 8 months is the rise in the average itself, which is the swap's effect once it has been shared among all 15 members. 15 years borrows the club size and calls it an age gap. 120 years multiplies correctly but keeps the answer in the wrong unit - 120 MONTHS is right, and that is 10 years, not 120.