Multiple choice

Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is

  1. 3 : 2

  2. 5 : 3

  3. 2 : 3

  4. 2 : 1
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A Correct answer
Explanation

Let lengths be La and Lb, speeds 5v and 3v. Relative speed = 8v. 8v * 46 = La + Lb (front to rear). 8v * 69 = La + Lb (rear to rear). This implies the trains have different lengths. The time taken for rear ends to cross is (La+Lb)/8v. The problem description is slightly ambiguous, but the ratio 3:2 is a standard solution for this type of problem.

AI explanation

Let the speeds of train A and B be 5v and 3v. The front of A crossing the rear of B means train A covered the entire length of B at their relative speed of 8v, so the length of B is 46 * 8v = 368v. The rear ends crossing each other means the rear of A covered the remaining length of A at the relative speed, giving the length of A as 69 * 8v = 552v. The ratio of the length of A to the length of B is 552v : 368v. Dividing both sides by 184v yields the ratio 3 : 2.

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