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      Question

      Age of 'X' four years ago from now was 50% less than

      the age of 'Y' four years hence from now. Twelve years hence from now, ratio of age of 'X' to 'Y' will be 4:5. Find the age of 'Y' four years ago from now.
      A 20 years Correct Answer Incorrect Answer
      B 22 years Correct Answer Incorrect Answer
      C 24 years Correct Answer Incorrect Answer
      D 26 years Correct Answer Incorrect Answer
      E 28 years Correct Answer Incorrect Answer

      Solution

      Let the present age of 'X' and 'Y' be 'm' and 'n' years, respectively. (m - 4) = 0.5 X (n + 4) Or, (m - 4) = (1/2) X (n + 4) Or, 2 X (m - 4) = n + 4 Or, 2m - 8 = n + 4 Or, 2m - n = 12 --------- (I) And, (m + 12) :(n + 12) = 4:5 Or, 5m + 60 = 4n + 48 Or, 4n - 5m = 12 ----------(II) On solving 5 X equation I + 2 X equation II, We get, 5 X (2m - n) + 2 X (4n - 5m) = 5 X 12 + 2 X 12 Or, 10m - 5n + 8n - 10m = 60 + 24 Or, 3n = 84 Or, 'n' = 28 Therefore, required age = 28 - 4 = 24 years

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