Multiple choice

Ratio of the speed of two trains of length 270 m each is 4 : 5. While travelling in opposite directions, they cross each other in 12 seconds. What is the speed of faster train?

  1. 72 kmph

  2. 80 kmph

  3. 90 kmph

  4. 95 kmph

  5. 108 kmph
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C Correct answer
Explanation

The relative speed is total distance divided by time: (270 + 270) / 12 = 540 / 12 = 45 m/s. Converting to kmph, 45 * 18/5 = 162 kmph. With a speed ratio of 4:5, the faster train is 5/9 of the total relative speed: 5/9 * 162 = 90 kmph.

AI explanation

When two trains travel in opposite directions, their relative speed is the sum of their individual speeds; let their speeds be 4x and 5x m/s. The total distance covered when crossing each other is the sum of their lengths, which is 270 plus 270, or 540 meters. Using the formula time equals distance divided by speed, 540 divided by 9x equals 12 seconds, so 9x equals 45 and x equals 5 m/s. The speed of the faster train is 5x, which is 25 m/s, and converting to kilometers per hour gives 25 multiplied by 18/5, resulting in 90 kmph.

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