Question

A man is 4 times as old as his son. After 16 years he will be only twice as old as his son. Find their present ages.

Answer 1

Let the present age of the son be x years.
As the man is 4 times as old as his son, the present age of the man will be (4x) years.
After 16 years:
Son's age = (x + 16) years
Man's age = (4x + 16) years

According to the question:
(4x + 16) = 2(x + 16)
or, 4x + 16 = 2 × x + 2 × 16 [On expanding the brackets]
or, 4x + 16 = 2x + 32
or, 4x − 2x = 32 − 16 [Transposing 16 to the R.H.S. and 2x to the L.H.S.]
or, 2x = 16
or, `(2x)/2=16/2` [Dividing both the sides by 2]
or, x = 8
∴ Present age of the son = 8 years
Present age of the man = 4x = 4 × 8
= 32 years