Multiple choice

A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph and passes them completely in 8 and 9 seconds respectively. The speed of the train is:

  1. 35 km/hr

  2. 45 km/hr

  3. 20 km/hr

  4. data inadequate

  5. None of these

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let train length = L meters, speed = v kmph. Speed in m/s = v × 5/18. Overtaking person at 2kmph: relative speed = (v-2) × 5/18 m/s. Time = 8s, so L = 8(v-2)(5/18). Overtaking person at 4kmph: relative speed = (v-4) × 5/18 m/s. Time = 9s, so L = 9(v-4)(5/18). Equating: 8(v-2) = 9(v-4), giving 8v - 16 = 9v - 36, so v = 20 kmph.