1.

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 `V_b`. A cyclist cycles from `A to B` with a uniform speed of `V_c`. A bus goes past the cyclist in `T_1` second in the direction `A to B` and every `T_2` second in the direction `B to A`. ThenA. `T_1 = (V_b T)/(V_b + V_c)`B. `T_2 = (V_b T)/(V_b - V_c)`C. `T_1 = (V_b T)/(V_b - V_c)`D. `T_2 = (V_b T)/(V_b + V_c)`

Answer» Correct Answer - C::D
(c.,d.) Distance between two buses on road is `V_bT`.
For `A to B` direction :
Distance = Relative velocity xx Time
`V_b T=(V_b - V_c)T_1 rArr T_1 = (V_b T)/(V_b - V_c)`
For `B to A` direction :
`V_b T =(V_b + V_c)T_2 rArr T_2 = (V_b T)/(V_b + V_c)`.


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