Question

13. Two towns A and B are connected by a regular bus
service with a bus leaving in either direction every T minutes.
A man cycling with a speed of 20 kmh-l in the direction A
o B notices that a bus goes past him every 18 min in the
lirection of his motion, and every 6 min in the opposite
irection. The period T of bus service is
.) 4.5 min
(b) 9 min
) 12 min
(d) 24 min​

Answer 1

ANSWER

Let the speed of each bus = v km/h

The distance between the nearest buses plying on either car = vT km...(i)

For buses going from town A to B:

Relative speed of bus in the direction of motion of man = (v - 20)

Buses plying in this direction go past the cyclist after every 18 min. Therefore, separation between the buses

= (v - 20)×(18/60)

From (i), (v - 20)×(18/60) = vT ...(ii)

For buses coming from B to A:

The relative velocity of bus with respect to man = (v + 20) Buses coming from town B past'the cyclist after every 6 min,

∴ (v + 20)×(6/60) = vT ...(iii)

Solving (ii) and (iii), we get\

v = 40 km/h and T = 2/30 h