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?

1. A. 15m
2. B. 18m
3. C. 20m
4. D. 24m

Answer: C

Explanation

Let the speed of the tram be ‘T’ km/hr and its length be ‘L’ meters.
When the tram overtakes a person moving in the same direction, the relative speed is the difference between their speeds. The distance covered is the length of the tram.

Convert speeds from km/hr to m/s by multiplying by 5/18.
Person X’s speed = 3 km/hr = 3 × (5/18) = 5/6 m/s.
Person Y’s speed = 4 km/hr = 4 × (5/18) = 10/9 m/s.
Let the tram’s speed be ‘t’ m/s.

For person X:
Relative speed = (t – 5/6) m/s.
Time taken = 8 seconds.
Length of tram (L) = Relative speed × Time = (t – 5/6) × 8 — (1)

For person Y:
Relative speed = (t – 10/9) m/s.
Time taken = 9 seconds.
Length of tram (L) = Relative speed × Time = (t – 10/9) × 9 — (2)

Equating (1) and (2):
8t – 40/6 = 9t – 90/9
8t – 20/3 = 9t – 10
10 – 20/3 = 9t – 8t
t = (30 – 20)/3 = 10/3 m/s.

Now substitute ‘t’ back into equation (1) to find L:
L = (10/3 – 5/6) × 8
L = (20/6 – 5/6) × 8
L = (15/6) × 8
L = (5/2) × 8
L = 20 meters.

This question tests the application of relative speed concepts in time, speed, and distance problems, specifically involving trains/trams overtaking objects, a common topic in UPSC CSAT.