The ratio between the speeds of A & B is 2:3, and therefore A takes 10 min more than the time taken by B to reach the destination. If A had walked at double the speed, he would have covered the distance in

A : B

$\mathrm{Speed}\to 2:3 (\because \mathrm{speed} \pm \frac{1}{\mathrm{Time}})$

$$\begin{gathered} \mathrm{Time} \to \underset{⏝}{3:2} \\ \boxed{\mathrm{difference}} \\ \downarrow \\ \boxed{10 \min } \end{gathered}$$

$\because$A takes time to reach the destination = 3 x 10 

= 30min  

If A had walked at double time speed, he would have covered the distance in half the time.

$=\frac{30}{2}=15\min$.