Multiple choice

Average age of the mother and her two sons is 27 years. Five years ago, the average age of the two sons was 12 years. If the difference between the ages of the two sons is four years, then the present age of the mother is -

  1. 34 years

  2. 47 years

  3. 64 years

  4. 27 years
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B Correct answer
Explanation

Current average of mother + 2 sons = 27, so their sum = 3 × 27 = 81 years. Five years ago, sons' average = 12, so their sum = 24, meaning their current sum = 24 + 10 = 34 (5 years each). Let sons be x and x+4 (difference 4). So x + (x+4) = 34, giving 2x = 30, x = 16. Sons are 16 and 20. Mother = 81 - 34 = 47 years.

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