Two towns `A` and `B` are connected by a regular bus service with a bus leaving in either direction every `T` min. `A` man cycling with a speed of `20 km h^(-1)` in the direction `A` to `B` notices that a bus goes past him every `18 min` in the direction of his motion, and every `6 min` in the opposite direction. What is the period `T` of the bus service and with what speed (assumed constant )do the buses ply on the road?

Options

A. `4.5minutes`
B. `24` minutes
C. 9minutes
D. 12 minutes

Answer

C

Explanation

Let distance between the buses be L
Velocity of man relative to bus moving in same direction `=v-u`
&velocity of man's relative to bus moving in opposite direction `=v+u`
`v-u=L//(18min)` & `v+u=L//(6min)`
on solving we get `u=v//2` Rightarrow `v=40` km//hr `{u=20km//hr(given)}`
` & L=18/60 (40-20)=6km`
Speed distance//time Rightarrow `40km//hr=60km//T Rightarrow T=9min`