Multiple choice

If a train runs at $40$ km/hr, it reaches its destination late by $11$ minutes, but if it runs at $50$ km/hr, it is late by $5$ minutes only. The correct time for the train to complete the journey is

  1. $13$ min
  2. $15$ min
  3. $19$ min
  4. $21$ min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D and time be T. D/40 = T + 11/60 and D/50 = T + 5/60. Subtracting: D/40 - D/50 = 6/60 = 1/10. D/200 = 1/10 => D = 20 km. Time taken at 40 km/h = 20/40 = 0.5 hours = 30 min. Since it is 11 min late, the correct time is 30 - 11 = 19 min.

AI explanation

Let the correct time for the journey be t minutes and the exact distance be D. Using the formula distance equals speed multiplied by time, the distance is 40 multiplied by (t + 11) divided by 60, and it also equals 50 multiplied by (t + 5) divided by 60. Equating the two expressions gives 40t plus 440 equals 50t plus 250, which results in 10t equals 190. The correct time to complete the journey is 19 minutes.

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