Multiple choice

The average age of 8 members of a committee is the same as it was 5 years ago, because an old member has been replaced by a young member. Find the age difference between the old member and the young member?

  1. 32 years

  2. 36 years

  3. 40 years

  4. 48 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the sum of ages be S. After 5 years, the sum would be S + 8*5 = S + 40. Replacing an old member (O) with a young member (Y) makes the sum S + 40 - O + Y. Since the average is the same, the sum is the same: S = S + 40 - O + Y. Thus, O - Y = 40.

AI explanation

When a replacement keeps the average the same over a period of 5 years for 8 members, the young member must offset the 5 years of age that every member gained. The total age increase that would have occurred is 8 times 5 = 40 years. Therefore, the young member must be 40 years younger than the old member. The result is 40 years.

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