Question

ten years ago the age of a was one third the age of b at that time.the present abe of b is 12 years more than the present age of a .the present age of a(in years) is

Answer 1

Let the age of A be x years
and the age of B be y years

According to the first condition,
$x - 10 = \frac{1 }{3} (y - 10) \\ 3(x - 10) = y - 10 \\ 3x - 30 = y - 10 \\ 3x - y = - 10 + 30 \\ 3x - y = 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (equation \: 1)$
according to second condition,
$y = 12 + x \\ - 12 = x - y \\ x - y = - 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: (equation \: 2)$

subtracting eqation 2 from 1, we get
$2x = 32 \\ x = 32 \div 2 \\ x = 16 \: years$
Present age of A is 16 years
Hope this helps you.