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Home Verbal Reasoning Problems on Ages See What Others Are Saying!
  • Question
  • The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. What are their present ages?


  • Options
  • A. 35 yeaas, 10 years
  • B. 36 years, 9 years
  • C. 37 years, 8 years
  • D. 39 years, 6 years

  • Correct Answer
  • 36 years, 9 years 

    Explanation

    Lt us assume the present age of father is P and son age is Q.
    According to question,
    P + Q = 45.................. (1)
    Five years ago, the father age = P - 5
    Five years ago, the son age = Q - 5
    According to question,
    Five years ago, the product of their ages was four times the father's age at that time.
    (P - 5) (Q - 5) = 4 (P - 5)
    PQ - 5P - 5Q + 25 = 4P - 20
    PQ - 5P - 5Q + 25 - 4P + 20 = 0
    ? PQ - 9P - 5Q + 45 = 0
    ? P(Q - 9) - 5(Q - 9) = 0
    ? (Q - 9) (P - 5) = 0
    ? (Q - 9) = 0 or (P - 5) = 0
    ? Q = 9 or P = 5
    Put the vale of Q in equation (1), we will get.
    if Q = 9 then P = 45 - 9 = 36 which is matched our answer.

    If P = 5 then Q = 45 - 5 = 40 years which is not match our answer.

    Method 2
    Let the present ages of father and his son be x and (45 - x) years respectively;
    then according to question,
    (x - 5) (45 - x - 5) = 4 (45 - x -5)
    ? x - 5 = 4
    ? x = 9
    Now, Father's age = 45 - x = 45 - 9 = 36 years


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