CDS 2026 (I) Elementary Mathematics, question 16

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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Q16

A train P starts from station X for station Y and another train Q starts from station Y for station X at the same time. After passing each other, P takes 4 hours to reach Y and Q takes 1 hour to reach X. If the average speed of P is 60 km/h, then what is the average speed of Q ?

  1. (a) 72 km/h
  2. (b) 80 km/h
  3. (c) 96 km/h
  4. (d) 120 km/hCorrect answer

Solution.

Answer: (d) 120 km/h

  1. Let the trains meet after t hours and let Q's speed be v.
  2. Before meeting, P covers 60t, which Q subsequently covers in 1 hour: v=60tv = 60t.
  3. Similarly, Q's pre-meeting distance vt equals P's remaining distance 60×4=24060 \times 4 = 240.
  4. Thus 60t2=24060t^{2} = 240, giving t=2t = 2 and v=120km/hv = 120km/h.
  5. Shortcut: For simultaneous starts, the speed ratio is the square root of the inverse ratio of post-meeting times: vQ/vP=4/1=2vQ/vP = \sqrt{4/1} = 2.