The respective ratio between A’s age two years ago and B’s age eight years hence, is 1 : 2. If A is eight years younger than B, what is B’s present age?

Let B’s present age be x years.

$herefore$ A’s present age = (x – 8) years

According to the question,

$frac{{x - 8 - 2}}{{x + 8}} = frac{1}{2}$

$Rightarrow$ 2x – 20 = x + 8

$Rightarrow$ 2x – x = 20 + 8

$Rightarrow$ x = 28 years