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?

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