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Question

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.

Options

A.$9\text{ }min,40\text{ }km/h$
B.$25\text{ }min,100\text{ }km/h$
C.$10\text{ }min,90\text{ }km/h$
D.$15\text{ }min,120\text{ }km/h$

Solution

$$X \rightarrow Y $$Let velocity of bus $= v\text{ }km/hr$

Relative velocity of bus w.r.t. scooty $= (v - 60)$

Distance between 2 consecutive buses $= vT$

$$\begin{array}{r} (v - 60)30 = vT\#(i) \end{array}$$

$$Y \rightarrow X$$

$$\begin{array}{r} (v + 60)10 = vT\#(ii) \end{array}$$

Equating (1) and (2)

$${(v - 60)30 = (v + 60)10 }{\therefore\ v = 120\text{ }km/hr }{T = 15\text{ }\min}$$

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