Question

A man is thrice as old as his son. Five years ago the man was four times 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 3 times as old as his son, the present age of the man will be (3x) years.

5 years ago:
Son's age = (x $-$ 5) years
Man's age = (3x $-$ 5) years

According to the question:
(3x $-$ 5) = 4(x $-$ 5)
or, 3x $-$ 5 = 4$\times$x $-$ 4$\times$5 [On expanding the brackets]
or, 3x $-$ 5 = 4x $-$ 20
or, 20 $-$ 5 = 4x $-$ 3x [Transposing 3x to the R.H.S. and 20 to the L.H.S.]
or, x = 15
∴ Present age of the son = 15 years
Present age of the man = 3x = 3$\times$15
= 45 years