Question:

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:

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To solve problems involving speed, distance, and time, use the relation \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).
Updated On: Aug 18, 2025
  • 80 kms
  • 40 kms
  • 70 kms
  • 30 kms
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The Correct Option is C

Solution and Explanation

Let the distance travelled by the train be \( d \) kms, and the time taken to travel this distance at the original speed is \( \frac{d}{40} \) hours. When the speed is reduced to 35 km/h, the time taken becomes \( \frac{d}{35} \) hours. According to the problem, the time difference is 15 minutes, or \( \frac{15}{60} = \frac{1}{4} \) hours. Thus, the time difference is: \[ \frac{d}{35} - \frac{d}{40} = \frac{1}{4} \] Solving for \( d \): \[ \frac{d}{35} - \frac{d}{40} = \frac{1}{4} \] \[ \frac{40d - 35d}{1400} = \frac{1}{4} \] \[ \frac{5d}{1400} = \frac{1}{4} \] \[ d = 70 \, \text{kms} \]
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