Multiple choice

Anju is waiting on the railway station for the arrival of her train. Two trains running in opposite directions cross Anju on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is

  1. 2 : 3

  2. 1 : 2

  3. 3 : 2

  4. 2 : 1
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C Correct answer
Explanation

Let lengths be L1, L2 and speeds be v1, v2. L1/v1 = 27, L2/v2 = 17. (L1+L2)/(v1+v2) = 23. Substituting L1=27v1 and L2=17v2: (27v1 + 17v2)/(v1+v2) = 23. 27v1 + 17v2 = 23v1 + 23v2. 4v1 = 6v2. v1/v2 = 6/4 = 3/2.

AI explanation

Let the trains have speeds $x$ and $y$, and Anju be a stationary point. Their lengths are $27x$ and $17y$ respectively. When crossing each other in 23 seconds moving in opposite directions, their relative speed is $(x + y)$, so the sum of their lengths equals $23(x + y)$. Equating the two expressions for total length gives $27x + 17y = 23x + 23y$. Rearranging this, $4x = 6y$, which means $x/y = 6/4 = 3/2$. The ratio of their speeds is 3 : 2.

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