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?

The man's present age is 65.

Step-by-step 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.

65

Step-by-step 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