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      Question

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

      respectively. Six years from now, the ratio of their ages will become 4:5 respectively. If 'Z' is 7 years older than 'Y', then what is the average current age (in years) of 'X' and 'Z'?
      A 20 yrs Correct Answer Incorrect Answer
      B 10 yrs Correct Answer Incorrect Answer
      C 25 yrs Correct Answer Incorrect Answer
      D 45 yrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

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

      So, (2n + 4 + 6) : (3n + 4 + 6) = 4:5

      Or, 5 × (2n + 10) = 4 × (3n + 10)

      Or, 10n + 50 = 12n + 40

      Or, 2n = 10

      Or, 'n' = 5

      Present age of 'X' = 2 × 5 + 4 = 14 years

      Present age of 'Y' = 3 × 5 + 4 = 19 years

      Present age of 'Z' = 19 + 7 = 26 years

      Required average = (14 + 26) ÷ 2 = 20 years

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