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…

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 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.

1. A. 9 min, 40 km/h
2. B. 25 min, 100 km/h
3. C. 10 min, 90 km/h
4. D. 15 min, 120 km/h (Correct answer)

Correct Answer

Option D — 15 min, 120 km/h

Detailed Solution & Explanation

The correct answer is 15 min, 120 km/h.

Key Points

• Let the bus speed be $v$. Spacing between consecutive buses $=vT$.
• Buses in the direction of motion (relative speed $v-60$) pass every 30 min: $(v-60)\cdot 30=vT$.
• Buses in the opposite direction (relative speed $v+60$) pass every 10 min: $(v+60)\cdot 10=vT$.
• Equating: $(v-60)30=(v+60)10\Rightarrow v=120$ km/h, and then $T=15$ min.