Tram overtaking two walkers - length
Question
A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?
Options
15 m
18 m
20 m
24 m
Explanation
Let the tram's speed be v km/hr and its length be L meters. Convert pedestrian speeds to m/s: X = 3 × (5/18) m/s, Y = 4 × (5/18) m/s. The relative speed of the tram passing a person is (v - person's speed). Since L = Relative Speed × Time, we can equate the tram lengths for both cases: ⟨MATH⟩(v - 3) × 5/18 × 8 = (v - 4) × 5/18 × 9⟨/MATH⟩. Cancel 5/18 from both sides: 8v - 24 = 9v - 36 \implies v = 12 km/hr. Substitute v back to find L: L = (12 - 3) × 5/18 × 8 = 9 × 40/18 = 20 meters.
Answer: (c).
Question details
Year
2025
Paper
CSAT
Question
Q19
Section
Numerical Ability
Sub-topic
Time, Speed & Distance
Type
Time-speed-distance
Difficulty
Hard
Source hint
Relative speed
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