UGC NET Paper 1 GA 2012 Dec Solved Paper

Let present age of A is x and B is y.
According to the question
$\mathit{x}+\mathit{y}=50$ …(i)
5 years ago, ratio of their age
$\frac{\mathit{x}-5}{\mathit{y}-5}=\frac{5}{3}$
$3\left(\mathit{x}-5\right)=5\left(\mathit{y}-5\right)$
or, $3\mathit{x}-5\mathit{y}=-10$ …(ii)
from (i) and (ii)
$8\mathit{x}=250-10$
$\mathit{x}=\frac{240}{8}=30$
$\mathit{y}=20$
Present Age of A = 30 years
Present Age of B = 20 years.