Multiple choice

Two trains each of length L are moving on parallel tracks with constant speeds. they take 40 s to overtake each other, if same trains are made to cross each other with earlier speeds then it requires just 20 s. ratio of speeds of the two trains is

  1. 1:1

  2. 2:1

  3. 3:1

  4. 4:1
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C Correct answer
Explanation

Let speeds be v1, v2. Overtaking: 2L / (v1-v2) = 40. Crossing: 2L / (v1+v2) = 20. Thus v1+v2 = 2(v1-v2). v1+v2 = 2v1-2v2, so v1 = 3v2. Ratio 3:1.

AI explanation

Let the speeds of the two trains be v1 and v2. When overtaking, the relative speed is v1 - v2 and the total distance is 2L, giving the equation 40 = 2L / (v1 - v2). When crossing each other in opposite directions, the relative speed is v1 + v2, giving 20 = 2L / (v1 + v2). Equating the distances yields 40(v1 - v2) = 20(v1 + v2), which simplifies to 2v1 - 2v2 = v1 + v2 and results in v1 = 3v2, making the ratio of their speeds 3:1.

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