Multiple choice

In a yoga class there were 12 members. Two members left the class and 4 new members joined. If the average age decreased by 4 years and the total age decreased by 2 years, what is the new average age of the class (In years)

  1. 22

  2. 27

  3. 26

  4. 23

  5. 18
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial total age be S and initial average be A = S/12. After changes, total members = 12 - 2 + 4 = 14. New total age = S - 2. New average = (S - 2) / 14 = A - 4. Substituting S = 12A, we get (12A - 2) / 14 = A - 4, leading to 12A - 2 = 14A - 56, so 2A = 54, A = 27. The new average is 27 - 4 = 23.

AI explanation

Let the initial average age be A, making the original sum of the ages of the 12 members equal to 12 multiplied by A. After two members leave and four join, the total number of members becomes 14, and their new sum of ages is 14 multiplied by (A - 4), which expands to 14A minus 56; this new sum is also given as the original sum minus 2 years, so 12A minus 2 equals 14A minus 56. Solving this equation gives an original average of 27 years, meaning the new average age of the class is 27 minus 4, which is 23 years.

Keep practicing — related questions