A and B are 15 km apart and when travelling towards each other meet after half an hour where as they meet two and a half hours later if they travel in the same direction. The faster of the two travels at the speed of :

Answer: Option B

Let the speed of A be x km/hr and speed of B be y km/hr
So, According to the question,
$$\begin{array}{rl}& \frac{15}{x+y}=\frac{1}{2}\\ & x+y=\mathrm{30.....}(i)\\ & \text{And,}\\ & \frac{15}{x-y}=\frac{5}{2}\\ & 5x-5y=\mathrm{30.....}(ii)\end{array}$$
Multiply equation (i) by 5 and add
$$\begin{array}{c}5x+5y=150\text{hfill}\\ 5x-5y=30\text{hfill}\\ \overline{10x=180}\text{hfill}\end{array}$$
$$\boxed{x=18\text{ km/hr}}$$

And y = 30 - $$x$$
⇒ y = 30 -18
⇒ y = 12 km/hr
∴ The faster travels at the speed of 18 km/hr