Question

At present a man is 5 times as old as his son, in 13 years time he will be three times as old as his son. Find the man's present age?

Answer 1

The man's present age is 65.

Explanation:

Let x = the man's age and y = his son's age.

In 13 yr, their ages will be x + 13 and y + 13, respectively.

We have two conditions:

(1) x = 5y

(2) x + 13 = 3(y + 13) Remove parentheses

x + 13 = 3y + 39 Subtract 13 from each side

(3) x = 3y + 26 Substitute (1) into (3)

5y = 3y + 26 Subtract 2y from each side

2y = 26 Divide each side by 2

(4) y = 13 Substitute (4) into (1)

x = 5 × 13

x = 65

The man's present age is 65.

Answer 2

65

Explanation:

let the son's age be x then the man's age is 5x

In 13 years

son's age = x + 13 and man's age = 5x + 13 and he is 3 times as old as son

5x + 13 = 3(x + 13)

5x + 13 = 3x + 39 ( subtract 3x from both sides )

2x + 13 = 39 ( subtract 13 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13 ← son's present age

5x = 5 × 13 = 65 ← man's present age