The time taken by Basha to complete each round of the circular track is?

Question

Akbar keeps running on a circular track with a uniform speed such that he completes one round every 40 seconds. On the same circular track Basha keeps running, but in the direction opposite to Akbar, with such uniform speed, that Akbar meets him every 15 seconds.

Answer 1

Hint

Suppose the track length is $C$.

The speed of Akbar is $$v_a=\frac{\text{distance travelled by Akbar in a round}}{\text{time taken}}=\ldots$$ (you can work out the rest yourself, leave it in $C$.)

The speed of Basha is $v_b$.

Assuming they start from the same place (which actually doesn't matter), you can think of it as they are $C$ units apart in a straight line.

So now you know that in the common time period $t_m=15 \text{ s}$, Akbar and Basha meet somewhere but their total distance is $C$. So you can form the equation using

$$\text{distance travelled by Akbar in $t_m$}+\text{distance travelled by Basha in $t_m$}=C$$

and solve for $v_b$.