Multiple choice

Choose the most appropriate option. A train which is moving at an average speed of $40$ kmph, reaches its destination on time. When its average speed reduces to $35$ kmph, then it reaches its destination $15$ minutes late. The distance travelled by the train is?

  1. $80$ kms
  2. $40$ kms
  3. $70$ kms
  4. $30$ kms
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be the distance. Time taken at 40 kmph is d/40, and at 35 kmph is d/35. The difference is 15 minutes, or 0.25 hours. So, d/35 - d/40 = 0.25. Solving this gives (8d - 7d)/280 = 0.25, so d = 280 * 0.25 = 70 km.

AI explanation

Let the correct time to reach the destination be t hours; since the distance is constant, 40 multiplied by t equals 35 multiplied by (t + 15/60). Solving 40t = 35t + 35/4 yields 5t = 35/4, so t is 7/4 hours. The distance travelled by the train is 40 multiplied by 7/4, which equals 70 kms.

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