Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?___

Let the present age of Barun be b years. Therefore, Arun's present age = 0.4b
Let Arun's age be half of Varun's after `k' years.
$0.4b+k=0.5(b+k)0.1b=0.5k\Rightarrow b=5k$
% increase in Varun's age during the preiod = $100\times \frac{(b+k)-b}{b}=100\times \left(\frac{k}{b}\right)=20$