Multiple choice

The age of Sarthak is one-fifth of the age of his mother and the 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 fathers age. Find the ratio of the present ages of Sarthak, 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 S, M, F be current ages. S = M/5, S+M = F. So F = M/5 + M = 6M/5. After 15 years: (S+15) + (M+15) = 4/3(F+15). Substitute S=M/5 and F=6M/5: (M/5 + M + 30) = 4/3(6M/5 + 15). 6M/5 + 30 = 8M/5 + 20. 10 = 2M/5, so M = 25. Then S = 5, F = 30. Ratio S:M:F = 5:25:30 = 1:5:6.

AI explanation

Let the present ages of Sarthak, his mother, and his father be S, M, and F. We are given S equals M divided by 5, so M equals 5S, and F equals S plus M, meaning F equals 6S. After 15 years, the equation is S plus 15 plus M plus 15 equals four-thirds times (F plus 15). Substituting M as 5S and F as 6S into the second equation yields 6S plus 30 equals four-thirds times (6S plus 15), which simplifies correctly for any S, so the ratio is 1 to 5 to 6.

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