Multiple choice

A train travelling with constant speed crosses a 96 metres long platform in 12 seconds and another 141 metres long platform in 15 seconds. The length of the train and its speed are

  1. 84 metres and 54 km/hour

  2. 64 metres and 54 km/hour

  3. 64 metres and 44 km/hour

  4. 84 metres and 60 km/hour
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A Correct answer
Explanation

Let train length be L and speed be V (m/s). (L + 96)/V = 12 and (L + 141)/V = 15. L + 96 = 12V and L + 141 = 15V. Subtracting gives 3V = 45, so V = 15 m/s. 15 m/s = 54 km/h. L = 12 * 15 - 96 = 180 - 96 = 84 meters.

AI explanation

Using the formula for crossing a platform where total distance equals the train length plus the platform length, we set up the equations T + 96 = 12s and T + 141 = 15s. Subtracting the first equation from the second gives 45 = 3s, meaning the speed s is 15 metres per second. Substituting s back yields T + 96 = 180, so the train length T is 84 metres. Converting the speed to kilometres per hour gives 15 multiplied by 18 over 5, which is 54 km/hour; therefore, the length is 84 metres and the speed is 54 km/hour.

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