Multiple choice

A train can travel $50\%$ faster than a car. Both start from point $A$ at the same time and reach point $B$, $75 km$ 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. $100 kmph$
  2. $120 kmph$
  3. $110 kmph$
  4. $130 kmph$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let car speed be v. Train speed is 1.5v. Time difference is 12.5 min = 12.5/60 = 5/24 hours. (75/v) - (75/1.5v) = 5/24. (75/v) - (50/v) = 5/24. 25/v = 5/24. v = 25 * 24 / 5 = 120 kmph.

AI explanation

Let the speed of the car be x km/hr, so the speed of the train is 1.5x km/hr. The time taken by the car to travel 75 km is 75/x hours, and the travel time for the train is 75/(1.5x) hours. Since the train lost 12.5 minutes, which is 5/24 hours, the equation is 75/x = 75/(1.5x) + 5/24. Simplifying this gives 75/x = 50/x + 5/24, which results in 25/x = 5/24, so x = 120. The speed of the car is 120 kmph.

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