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      Question

      Age of 'P' two years ago from now was 50% less than the

      age of 'Q' six years hence from now. Eight years hence from now, ratio of age of 'P' to 'Q' will be 4:5. Find the age of 'Q' two years ago from now.
      A 18 years Correct Answer Incorrect Answer
      B 20 years Correct Answer Incorrect Answer
      C 22 years Correct Answer Incorrect Answer
      D 24 years Correct Answer Incorrect Answer
      E 26 years Correct Answer Incorrect Answer

      Solution

      Let the present age of 'P' and 'Q' be 'm' and 'n' years, respectively. (m - 2) = 0.5 X (n + 6) Or, (m - 2) = (1/2) X (n + 6) Or, 2 X (m - 2) = n + 6 Or, 2m - 4 = n + 6 Or, 2m - n = 10 --------- (I) And, (m + 8) :(n + 8) = 4:5 Or, 5m + 40 = 4n + 32 Or, 4n - 5m = 8 ----------(II) On solving 5 X equation I + 2 X equation II, We get, 5 X (2m - n) + 2 X (4n - 5m) = 5 X 10 + 2 X 8 Or, 10m - 5n + 8n - 10m = 50 + 16 Or, 3n = 66 Or, 'n' = 22 Therefore, required age = 22 - 2 = 20 years

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