Two cities X and Y are connected by a regular bus service with a bus… | NEET 2025

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Relative Velocity

Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. A girl is driving scooty with a speed of $60\text{ km/h}$ in the direction $X$ to $Y$ 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 $T$ of the bus service and the speed (assumed constant) of the buses.

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Answer: (b)

Bus speed $v$ ; buses in each direction are spaced $vT$ apart.
Same direction: $\frac{vT}{v - 60} = 30\text{ min}$ ; opposite: $\frac{vT}{v + 60} = 10\text{ min}$
Divide: $\frac{v + 60}{v - 60} = 3 \Rightarrow v = 120\text{ km/h}$
$\frac{120T}{60} = 30 \Rightarrow T = 15\text{ min}$
So the answer is (b) 15 min, 120 km/h.

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