Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:*1 point3:4None of these3:21:3

The problem involves two trains crossing a man and each other. We can solve this problem by using the concept of relative speed.

Step 1: Let's denote the speed of the first train as 'a' and the speed of the second train as 'b'. The speeds are in some arbitrary units.

Step 2: When the trains cross the man standing on the platform, they cover their own length. So, the time taken to cross the man is the time taken to cover their own length. Therefore, we can write the speeds of the trains as:

Speed of first train = Length of first train / Time taken by first train to cross the man = a / 27 Speed of second train = Length of second train / Time taken by second train to cross the man = b / 17

Step 3: When two trains cross each other running in opposite directions, they cover the sum of their lengths. The time taken to cross each other is the time taken to cover the sum of their lengths. Therefore, we can write:

Speed of first train + Speed of second train = (Length of first train + Length of second train) / Time taken by trains to cross each other

Substituting the values from step 2, we get:

(a / 27) + (b / 17) = (a + b) / 23

Step 4: Solving the equation from step 3, we get the ratio of their speeds as:

a : b = 3 : 4

So, the ratio of their speeds is 3:4.