A and B started from X and Y respectively at the same time in the opposite directions. After meeting, A took 2.7 hours to reach Y and B took 1.2 hours to reach X. If the speed of B is 48 km/h, what is the speed of A(in km/h)?

We know,

$$\frac{Speed\ of\ A\ }{Speed\ of\ B}=\sqrt{\frac{time\ taken\ by\ B\ }{Time\ taken\ by\ A}}$$

Speed of B = 48km/hr

Time taken by A = 2.7 hrs

Time taken by B = 1.2 hrs

Lets putting these values in above formula ; 

$$\frac{Speed\ of\ A\ }{48}=\sqrt{\frac{1.2\ }{2.7}}$$

$$\frac{Speed\ of\ A\ }{48}=\sqrt{\frac{4\ }{9}}=\frac{2}{3}$$

$$Speed\ of\ A\ =\frac{\left(48\times\ 2\right)}{3}=32\ \frac{km}{hrs}$$

hence, Option A is correct.