Multiple choice

In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is $9$ years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

  1. $40$ years
  2. $50$ years
  3. $45$ years
  4. $60$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let daughter = D, son = S, father = F, mother = M. F = 3D. S = M/2. M = F - 9. S = D + 7. Substituting: (F-9)/2 = D+7 => F-9 = 2D+14 => F = 2D+23. Since F = 3D, 3D = 2D+23, so D = 23. Then F = 69. M = 69 - 9 = 60.

AI explanation

Let the ages of the father, daughter, son, and mother be F, D, S, and M. From the given information, S - D = 7 and D = S - 7. Since the father is three times as old as his daughter, F = 3(S - 7). Because the wife is 9 years younger than her husband, M = F - 9, so M = 3(S - 7) - 9 = 3S - 30. Since the son is half his mother's age, M = 2S, leading to 2S = 3S - 30, meaning S = 30. The mother's age is twice the son's age, which is 60.

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