Question

Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age

Answer 1

Let the age of a man be “x” and the age of a son be “y”
5 years ago

Age of a man = x – 5 years

Age of his son = y – 5 years

By the given first condition

x – 5 = 7(y – 5)

x – 5 = 7y – 35

x – 7y = – 35 + 5

x – 7y = – 30 → (1)

Five years hence

Age of a man = x + 5 years

Age of his son = y + 5 years

By the given second condition

x + 5 = 4(y + 5)

x + 5 = 4y + 20

x – 4y = 20 – 5

x – 4y = 15 → (2)

(1) – (2) ⇒ – 3y = – 45

3y = 45

y = `45/3`

= 15

Substitute the value of y = 15 in (1)

x – 7(15) = – 30

x – 105 = – 30

x = – 30 + 105

= 75

Age of the man is 75 years

Age of his son is 15 years