Question

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

Options

• 2: 3

• 1: 2

• 3: 2

• 2: 1

Answer 1

3: 2

Explanation:

Let the length of two trains are l and m.

Then, Speed of first train = `l/27` m/sec

Speed of second train = `"m"/17` m/sec

Again, two train crosses each other in 23 sec.

So, `(l/27 + m/27)xx 23 = l + m`

(17 l + 27 m) 23 = 27 × 17 (l + m)

Dividing both sides by m, we get.

`(17 l/m + 27) xx 23 = 27 xx 17 (l/m + 1)`

`17 xx 23 l/m + 27 xx 23 = 27 xx 17 l/m + 27 xx 17`

17 (27 - 23) `l/m` = 27 (23 - 17)

`17 xx 4 l/m = 27 xx 6`

`l/m xx 17/27 = 6/4`

or, `(l/27)/(m/17) = 3/2`

Hence, ratio of their speed = 3 :2