Multiple choice

The age of the boy is one-fifth of the age of his mother and sum of the ages of the son and the mother is equal to the age of the father. After 15 years, the sum of the ages of the son and his mother will be four-third of his father's age. Find the ratio of the present ages of son, mother and father, respectively.

  1. 1 : 5 : 7

  2. 2 : 10 : 10

  3. 1 : 5 : 6

  4. 2 : 8 : 9
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C Correct answer
Explanation

Let son = S, mother = M, father = F. S = M/5, so M = 5S. S + M = F, so F = 6S. After 15 years: (S + 15) + (M + 15) = (4/3)(F + 15). Substitute M=5S, F=6S: 6S + 30 = (4/3)(6S + 15) = 8S + 20. 2S = 10, S = 5. Then M = 25, F = 30. Ratio S:M:F = 5:25:30 = 1:5:6.

AI explanation

Let the present ages of the son, mother, and father be S, M, and F. We are given S + M = F and S + M + 30 = (4/3)(F + 15). Substituting F for S + M in the second equation gives F + 30 = (4/3)F + 20, which results in F/3 = 10, so F is 30. Since S is one-fifth of M, let their ages be x and 5x; given x + 5x = 30, x is 5. Their present ages are 5, 25, and 30, making the ratio 1 : 5 : 6.

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