Two cities X and Y are connected by a regular bus service with a bus leaving in either direction eve

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NEET is a competitive examination conducted in India. This question is from the 2025 NEET Physics paper.

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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 a scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. The period T of the bus service and the speed of the buses are respectively:

Accepted Answer

Correct Answer: A — 15 min, 120 km/hStep-by-step Solution:Let v = speed of buses (km/h), T = time interval between consecutive buses (min).Distance between two consecutive buses (in the same direction) = vT (in consistent units).Buses going in same direction (X → Y):Relative speed of bus w.r.t. scooty = (v − 60) km/hTime between consecutive buses passing the scooty = vT/(v − 60) = 30 min ...(i)Buses coming in opposite direction (Y → X):Relative speed = (v + 60) km/hTime between consecutive buses = vT/(v + 60) = 10 min ...(ii)Dividing (i) by (ii): (v + 60)/(v − 60) = 3v + 60 = 3v − 180 → 2v = 240 → v = 120 km/hFrom (ii): 120T/(120 + 60) = 10 → 120T/180 = 10 → T = 10 × 180/120 = 15 minKey Concepts from Motion in a Straight Line (NCERT Class 11, Chapter 3):Relative velocity: When two objects move in the same direction, relative speed = v₁ − v₂. When moving in opposite directions, relative speed = v₁ + v₂.This is a classic problem combining relative velocity with the concept of distance between consecutive objects (waves or buses).The distance between consecutive buses = vT (speed × time interval). This 'distance' is fixed regardless of reference frame but the time to observe it changes with relative motion.

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