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 ?
- (a) 15 m
- (b) 18 m
- (c) 20 m ✓ UPSC's answer
- (d) 24 m
Why the answer is (c)
• Let the speed of the tram be $v$ km/hr and its length be $L$ meters.
• The relative speed with person X (3 km/hr) is $(v - 3)$ km/hr, and with person Y (4 km/hr) is $(v - 4)$ km/hr.
• Convert relative speeds to m/s by multiplying by $5/18$: $v_x = (v-3) \times \frac{5}{18}$ and $v_y = (v-4) \times \frac{5}{18}$.
• The time to pass is given by $\text{Time} = \frac{\text{Length}}{\text{Relative Speed}}$. Thus, $8 = \frac{L}{(v-3) \times \frac{5}{18}}$ and $9 = \frac{L}{(v-4) \times \frac{5}{18}}$.
• Simplifying gives $L = 8 \times (v-3) \times \frac{5}{18}$ and $L = 9 \times (v-4) \times \frac{5}{18}$.
• Equating the two expressions for $L$: $8(v-3) = 9(v-4) \Rightarrow 8v - 24 = 9v - 36 \Rightarrow v = 12$ km/hr.
• Substituting $v=12$ into the first equation: $L = 8 \times (12-3) \times \frac{5}{18} = 8 \times 9 \times \frac{5}{18} = 4 \times 5 = 20$ meters.
Why the other options are wrong
- (a) 15 m
- 15 m is incorrect because it does not satisfy the time-distance relationship derived from the relative speeds of 9 km/hr and 8 km/hr.
- (b) 18 m
- 18 m is incorrect because it results from an arithmetic error in solving for the tram's speed or length.
- (d) 24 m
- 24 m is incorrect because it does not match the calculated length of 20 m based on the given times and walking speeds.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.