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      Question

      The sum of the ages of a father and his son is 54 years.

      Six years ago, the father was 5 times as old as his son. Find their present ages.
      A 77 yrs and 33 yrs Correct Answer Incorrect Answer
      B 69 yrs and 27 yrs Correct Answer Incorrect Answer
      C 41 yrs and 13 yrs Correct Answer Incorrect Answer
      D 51 yrs and 19 yrs Correct Answer Incorrect Answer

      Solution

      Let present age of father = F years Let present age of son = S years Given: F + S = 54 ...(1) Six years ago: Father’s age = F − 6 Son’s age = S − 6 Given: F − 6 = 5(S − 6) ⇒ F − 6 = 5S − 30 ⇒ F = 5S − 24 ...(2) Substitute (2) in (1): (5S − 24) + S = 54 6S − 24 = 54 6S = 78 S = 13 Then F = 54 − 13 = 41 Answers: Father’s present age = 41 years Son’s present age = 13 years

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