From two places, 60 km apart A and B start towards each other at the same time and meet each other after 6 hours. If A travelled with 2/3 of his usual speed and B travelled with double of his speed they would have meet after 5 hours. The speed of A is :

Answer: Option B

$$\because$$ They meet after 6 hours if they walk towards each other i.e., their speed will be added.
So, their relative speed in opposite direction
$$=\frac{\text{Distance }}{\text{Time }}=\frac{60}{6}$$
Relative speed in opposite direction :
$$\left(\rightleftharpoons \right)=10\text{ km/h}.....\text{(i)}$$
According to the question,
$$\begin{array}{rl}& \Rightarrow \frac{2}{3}A+2B=\frac{60}{5}\\ & \Rightarrow \frac{2}{3}A+2B=12\\ & \Rightarrow A+3B=18\\ & \Rightarrow B^{\prime }s\text{ Speed = }\frac{18-A}{3}\\ & \Rightarrow A+B=10\\ & \Rightarrow A+\frac{18-A}{3}=10\\ & \Rightarrow 3A+18-A=30\\ & \Rightarrow 2A=12\\ & \Rightarrow A\text{’s speed = 6 km/h}\end{array}$$