NEET 2025 — Physics solution

NEET2025Physics

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 a scooty with a speed of $60$ 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.

A
9 min, 40 km/h
B
25 min, 100 km/h
C
10 min, 90 km/h
D
15 min, 120 km/h

Solution

Let bus speed be $V_{B}$ and scooty speed $V_{S} = 60$ km/h. The distance between consecutive buses on the road is $D = V_{B} \cdot T$ .

Same direction (overtaking): $D = (V_{B} - V_{S}) \cdot t_{1}$ with $t_{1} = 30$ min $= 1/2$ hr.

Opposite direction: $D = (V_{B} + V_{S}) \cdot t_{2}$ with $t_{2} = 10$ min $= 1/6$ hr.

$(V_{B} - 60) \cdot \frac{1}{2} = (V_{B} + 60) \cdot \frac{1}{6} \Rightarrow 3 (V_{B} - 60) = V_{B} + 60 \Rightarrow 2 V_{B} = 240 \Rightarrow V_{B} = 120$ km/h.

$D = (120 - 60) \cdot \frac{1}{2} = 30$ km. $T = D / V_{B} = 30/120 = 1/4$ hr $= 15$ min.

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