Multiple choice

The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?

  1. 30 years

  2. 24 years

  3. 26 years

  4. 22 years

  5. 36 years
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A Correct answer
Explanation

Let the sum of ages of the 8 men be S. The new sum is S - 20 - 24 + W1 + W2 = S + 16 (since average increases by 2, total increases by 8 * 2 = 16). Thus, W1 + W2 = 16 + 44 = 60. The average age of the two women is 60 / 2 = 30.

AI explanation

The average age of 8 men increases by 2 years, meaning the total age of the group increases by 8 multiplied by 2, which is 16 years. The total age of the two replaced men is 20 plus 24, giving 44 years. The total age of the two women must be 16 years more than the men, so 44 plus 16 equals 60 years. The average age of the women is 60 divided by 2, which is 30 years.

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