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      Question

      Five years ago, the ratio of ages of 'X' and 'Y' was 2:3,

      respectively. Seven years from now, the ratio of their ages will be 4:5, respectively. If 'Z' is eight years elder than Y, then find the average present age (in years) of 'X' and 'Z'.
      A 24 yrs Correct Answer Incorrect Answer
      B 18 yrs Correct Answer Incorrect Answer
      C 28 yrs Correct Answer Incorrect Answer
      D 12 yrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the age of 'X' and 'Y' five years ago be '2n' and '3n' years, respectively.

      So, (2n + 5 + 7) : (3n + 5 + 7) = 4:5

      Or, 5 × (2n + 12) = 4 × (3n + 12)

      Or, 10n + 60 = 12n + 48

      Or, 2n = 12

      Or, n = 6

      Present age of 'X' = 2 × 6 + 5 = 17 years

      Present age of 'Y' = 3 × 6 + 5 = 23 years

      Present age of 'Z' = 23 + 8 = 31 years

      Required average = (17 + 31) ÷ 2 = 24 years

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