Multiple choice

A couple has a son and a daughter. The age of the father is four times that of the son and the age of the daughter is one-third of that of her mother. The wife is 6 years younger to her husband and the sister is 3 years older than her brother. The mother's age is ?

  1. 48 years

  2. 42 years

  3. 54 years

  4. 63 years

  5. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

F = 4S. D = M/3. W = F - 6. D = S + 3. Substitute D: (S + 3) = M/3 => M = 3S + 9. F = 4S. W = 4S - 6. Since W = M, 4S - 6 = 3S + 9 => S = 15. F = 60. W = 60 - 6 = 54.

AI explanation

Let the son's age be S, the father's age be F, the daughter's age be D, and the mother's age be M. We know F = 4S, D = M / 3, F = M + 6, and D = S + 3. Substituting F from the third equation into the first gives M + 6 = 4S. Since D = S + 3 and D = M / 3, we have S = M / 3 - 3. Substituting this into M + 6 = 4(M / 3 - 3) gives M + 6 = 4M / 3 - 12. Solving this yields 18 = M / 3, so the mother's age is 54 years.

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