A train can travel 50% faster than a car. Both start from point A at the same…

2024

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

  1. A.

    100 kmph

  2. B.

    110 kmph

  3. C.

    120 kmph

  4. D.

    130 kmph

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Correct answer: C

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Let the speed of the car be x km/h.

  1. Train speed = 50% faster = 1.5x = (3/2)x km/h.

  2. Time taken by the car = distance/speed = 75/x hours.

  3. Running time of the train = 75 / ((3/2)x) = 50/x hours.

  4. Train stoppage = 12.5 minutes = 12.5/60 = 5/24 hours.

  5. They arrive together, so: 75/x = 50/x + 5/24.

  6. Rearrange: 75/x − 50/x = 5/24 ⇒ 25/x = 5/24 ⇒ x = 25 × 24/5 = 120.

  7. Therefore the speed of the car is 120 kmph.

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