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      Question

      The present age ratio of a father to his son is 15:7,

      and that of a mother to her daughter is 6:2. The mother is three years younger than the father, and the daughter is four years younger than the son. Find the mother’s age 10 years from now.
      A 29.5 yrs Correct Answer Incorrect Answer
      B 21.5 yrs Correct Answer Incorrect Answer
      C 18.5 yrs Correct Answer Incorrect Answer
      D 12.5 yrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let present age of father and son be 15m and 7m years respectively, and mother and daughter be 6n and 2n years respectively. Now, 15m - 6n = 3 ------------ (I) 7m - 2n = 4 ------------- (II) Now solving I - 3 × II: 15m - 6n - 3(7m - 2n) = 3 - 12 15m - 6n - 21m + 6n = -9 -6m = -9 m = 1.5 Put in equation II: 7 × 1.5 - 2n = 4 10.5 - 2n = 4 2n = 6.5 n = 3.25 Required age = 6 × 3.25 + 10 = 29.5 years

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