Multiple choice

A man covered a distance of 200 km by train and bus. He covered 160 km by train and 40 km by bus, and it took him 3 hours in it. If he had covered half the distance by train and half by bus, it would have taken him him 3 hours and 45 minutes. Find the speed of train.

  1. 40 kmph

  2. 50 kmph

  3. 60 kmph

  4. 80 kmph

  5. 100 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train speed be x and bus speed be y. 160/x + 40/y = 3. Also 100/x + 100/y = 3.75 (3 hours 45 mins). Solving this system: 100/x + 100/y = 15/4 => 1/x + 1/y = 15/400 = 3/80. From first: 4/x + 1/y = 3/40. Subtracting: 3/x = 3/40 - 3/80 = 3/80, so x = 80.

AI explanation

Let the speed of the train be x km/hr and the speed of the bus be y km/hr. We establish the equations 160/x + 40/y = 3 and 100/x + 100/y = 3.75 from the given scenarios. Substituting 1/x = a and 1/y = b, we get 160a + 40b = 3 and 100a + 100b = 3.75. Solving this system of equations gives a = 1/80 and b = 1/50. Therefore, the speed of the train is 80 kmph.

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