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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