Four years ago the average age of a family of 5 was 24 years. Nobody has joined or left the family since. What is the average age of the family today?

Every one of the five people has gained exactly 4 years, so the average gains 4 years too: 24 + 4 = 28 years. (The total rose from 120 to 140, and 140/5 = 28.) 24.8 spreads a single lot of 4 years over the 5 people - but each person aged 4 years, not the family as a whole. 44 adds the total gain of $5\times 4=20$ years to the AVERAGE instead of to the total. 24 assumes the average stands still, which would only happen if nobody aged.