Two cities A and B are connected by a regular bus service with buses plying in either direction every T seconds. The speed of each bus is uniform and equal to Vb. A cyclist cycles from A to B with a uniform speed of Vc. A bus goes past the cyclist in T1 second in the direction A to B and every T2 second in the direction B to A. Then
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a
T1=VbTVb+Vc
b
T2=VbTVb−Vc
c
T1=VbTVb−Vc
d
T2=VbTVb+Vc
answer is C.
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Detailed Solution
Distance between two buses on road is VbT. For A to B direction: Distance = Relative velocity × Time VbT=Vb−VcT1⇒T1=VbTVb−VcFor B to A direction: VbT=Vb+VcT2 ⇒ T2=VbTVb+Vc