Question

Five years ago a man was seven times as old as his son. Five years hence , the father will be three times asa old as his son. Find their present age.

Answer 1

Let the present age of son be x
and present age of father be y
$5 \: years \: \: ago \\ y - 5 = 7(x - 5) \\ 7x - y = 30 - - - (1) \\ 5 \: years \: \: after \\ y + 5 = 3(x + 5) \\ 3x - y = - 10 - - - (2) \\ (1) - (2) \: gives \\ 4x = 40 \\ x = 10 \\ from \: (1) \\ y = 7 \times 10 - 30 = 40$