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UPSC Prelims 2025 CSAT, question 39

Topic: Arithmetic

Q39

A tram overtakes 2 persons XX and YY 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) 15 m
  2. (b) 18 m
  3. (c) 20 mCorrect answer
  4. (d) 24 m

Solution.

Answer: (c) 20 m

  1. Let the speed of the tram be vv km/hr; since the tram covers its own length LL relative to both walkers, (v−3)×8=(v−4)×9(v - 3) \times 8 = (v - 4) \times 9.
  2. Solving 8v−24=9v−368v - 24 = 9v - 36 gives v=12v = 12 km/hr.
  3. Converting v−3=9v - 3 = 9 km/hr to m/s gives 9×518=2.59 \times \frac{5}{18} = 2.5 m/s, so the length of the tram is L=2.5×8=20L = 2.5 \times 8 = 20 m.