Question

Five years ago a man was 7 Times as olld as his son.Five years hence he will be 3 times as old as his son. Find their present ages

Answer 1

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