Question

Five years ago, A was thrice as old as B and ten years later A shall be twice as old as B. what are the present ages of A and B.?

Answer 1

The answer is A = 50 years and B = 20 years

Answer 2

Let the present age of A be x and
present age of B be y
$five \: \: years \: \: ago \\ x - 5 = 3(y - 5) \\ x - 3y = - 10 - - - (1) \\ten \: \: years \: \: later \\ x + 10 = 2(y + 10) \\ x - 2y = 10 - - - (2) \\ (2) - (1) \: \: gives \\ y= 20 \\ from \: \: (1) \\ x = 3 \times 20 - 10 = 50$