Multiple choice

An express train left Delhi for Howrah at $3$ pm at an average speed of $60$ km/hr. At $1$ pm a goods train also had left Delhi for Howrah on a parallel track at an average speed of $40$ km/hr. How far from Delhi is the express train expected to overtake the goods train?

  1. $200$ km
  2. $220$ km
  3. $240$ km
  4. $280$ km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Goods train starts at 1 pm, Express at 3 pm. By 3 pm, goods train has traveled 2 hours * 40 km/hr = 80 km. Relative speed = 60 - 40 = 20 km/hr. Time to overtake = 80 km / 20 km/hr = 4 hours. Distance from Delhi = 60 km/hr * 4 hours = 240 km.

AI explanation

The express train leaves 2 hours after the goods train, meaning the goods train has a 40 times 2 kilometer head start, totaling 80 km. The express train travels at a relative speed of 60 minus 40, which is 20 km/hr, to catch up to the goods train. The time needed to close the 80 km gap is 80 divided by 20, equaling 4 hours. The overtaking distance from Delhi is the express train's speed multiplied by this time, giving 60 times 4, which is 240 km.

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