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 $$\frac{2}{3}$$ of his usual speed and B travelled with double of his speed they would have meet after 5 hours. The speed of A is :

Solution(By Examveda Team)

$$\because $$ 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,
$$\eqalign{ & \Rightarrow \frac{2}{3}A + 2B = \frac{{60}}{5} \cr & \Rightarrow \frac{2}{3}A + 2B = 12 \cr & \Rightarrow A + 3B = 18 \cr & \Rightarrow B's{\text{ Speed = }}\frac{{18 - A}}{3} \cr & \Rightarrow A + B = 10 \cr & \Rightarrow A + \frac{{18 - A}}{3} = 10 \cr & \Rightarrow 3A + 18 - A = 30 \cr & \Rightarrow 2A = 12 \cr & \Rightarrow A{\text{'s speed = 6 km/h}} \cr} $$