Multiple choice

There are 24 persons in a club. When three new members, whose average age is one-fourth of the average age of the initial group of 24 persons joined the club, the average age of all the members in the club decreased by 3 years. What is the average age (in years) of all the 27 members in the club?

  1. 9

  2. 33

  3. 36

  4. 42
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A be the average of 24 persons. Total age = 24A. New members average = A/4. Total age of 3 new members = 3 * (A/4) = 0.75A. New total age = 24.75A. New average = 24.75A / 27 = A - 3. 24.75A = 27A - 81. 2.25A = 81. A = 36. New average = 36 - 3 = 33.

AI explanation

Let the initial average age of the 24 members be A. The total age of the initial group is 24A, and the total age of the three new members is 3 times one-fourth of A, which is 0.75A. The new average age of all 27 members becomes A minus 3. Setting up the equation (24A + 0.75A) divided by 27 equals A minus 3, we solve to find A equals 36. Therefore, the new average age of all 27 members is 36 minus 3, which is 33 years.

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