Two cities and are connected by a regular bus service with a bus leaving in either direction every min. A girl is driving scooty with a speed of in the direction to notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period of the bus service and the speed (assumed constant) of the buses.
- A
- B
- C
- D
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Correct answer: B

$$\begin{aligned} \& \text { Let velocity of bus }=v \mathrm{~km} / \mathrm{hr} \\ \& \text { Relative velocity of bus w.r.t. scooty }=(v-60) \\ \& \text { Distance between } 2 \text { consecutive buses }=v T \\ \& (v-60) 30=v T \quad\text{.... (i)}\\ \& Y \rightarrow X \\ \& (v+60) 10=v T \quad\text{.... (ii)}\\ \& \text { Equating }(1) \text { and }(2) \\ \& (v-60) 30=(v+60) 10 \\ \& \therefore \quad v=120 \mathrm{~km} / \mathrm{hr} \\ \& T=15 \mathrm{~min} \end{aligned}$$
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