Q) The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.

Ans: Let’s consider the father’s age is X and son’s age is Y.

Step 1: It is given that, X + Y = 45 …… (i)

∴ Y = 45 – X

Step 2: 

5 years ago, age of father = X – 5

and 5 years ago, age of son = Y – 5

Given that, (X – 5) (Y – 5) = 124

By substituting, value of Y in the above equation, we get:

(X – 5) (45 –  X – 5) = 124

(X – 5) (40 –  X) = 124

40 X – 200 – X² + 5 X = 124

X² – 45 X + 324 = 0

(X – 36) (X – 9) = 0

X = 36 and X = 9

Therefore, value of Y = 45 – 36 = 9 and 45 – 9 = 36 respectively

Since son’s age will be less than father’s age, i.e. Y < X

Hence, value of X 9,

X = 36 and Y = 9

Therefore, the father’s age if 36 and son’s age will be 9.