Multiple choice

A train passes two persons who are walking in the direction opposite to the direction of train at the rate of 10 m/s and 20 m/s respectively in 12 seconds and 10 seconds, respectively. Find the length of the train.

  1. 400

  2. 500

  3. 600

  4. 700
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C Correct answer
Explanation

Let L be the length of the train and v be its speed. The relative speed against the first person is (v + 10) and against the second is (v + 20). Using distance = speed * time, we have L = 12(v + 10) and L = 10(v + 20). Solving 12v + 120 = 10v + 200 gives 2v = 80, so v = 40. Substituting back, L = 12(40 + 10) = 600.

AI explanation

Since the people are walking opposite to the train, we use the relative speed concept where their speeds add to the train's speed. Let the train's length be L and its speed be V; for the first person, L divided by (V plus 10) equals 12 seconds, and for the second person, L divided by (V plus 20) equals 10 seconds. Solving these equations, 12V plus 120 equals 10V plus 200, meaning the train's speed V is 40 m/s. Substituting this back gives the train's length as 12 multiplied by (40 plus 10), which is 600 meters.

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