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:

Let's denote the speeds of the two trains as S1 and S2, and their lengths as L1 and L2 respectively.

Step 1: When a train passes a man standing on the platform, the distance covered is equal to the length of the train. So, we can write the following equations from the given information:

L1 = 27S1 ...(equation 1) L2 = 17S2 ...(equation 2)

Step 2: When two trains cross each other running in opposite directions, the distance covered is equal to the sum of their lengths. So, we can write:

(L1 + L2) = 23*(S1 + S2) ...(equation 3)

Step 3: Substitute equation 1 and 2 into equation 3, we get:

27S1 + 17S2 = 23*(S1 + S2)

Step 4: Simplify the equation to find the ratio of their speeds S1/S2:

27S1 + 17S2 = 23S1 + 23S2 4S1 = 6S2 S1/S2 = 6/4 = 3/2

So, the ratio of their speeds is 3:2.

Let's denote the speeds of the two trains as S1 and S2, and their lengths as L1 and L2 respectively.

Step 1: When a train passes a man standing on the platform, the distance covered is equal to the length of the train. So, we can write the following equations according to the problem:

L1 = 27S1 ...(equation 1) L2 = 17S2 ...(equation 2)

Step 2: When two trains cross each other running in opposite directions, the distance covered is equal to the sum of their lengths. So, we can write:

(L1 + L2) = 23*(S1 + S2) ...(equation 3)

Step 3: Substitute equation 1 and 2 into equation 3, we get:

27S1 + 17S2 = 23*(S1 + S2)

Step 4: Simplify the equation, we get:

4S1 = 6S2

Step 5: So, the ratio of their speeds S1:S2 is 6:4, which simplifies to 3:2.

Let's denote the speeds of the two trains as S1 and S2, and their lengths as L1 and L2 respectively.

Step 1: When a train passes a man standing on the platform, the distance covered is equal to the length of the train. So, we can write the following equations according to the problem:

L1 = 27S1 ...(equation 1) L2 = 17S2 ...(equation 2)

Step 2: When two trains cross each other running in opposite directions, the distance covered is equal to the sum of their lengths. So, we can write:

(L1 + L2) = 23*(S1 + S2) ...(equation 3)

Step 3: Substitute equation 1 and 2 into equation 3, we get:

27S1 + 17S2 = 23*(S1 + S2)

Step 4: Simplify the equation, we get:

4S1 = 6S2

Step 5: So, the ratio of their speeds S1:S2 is 6:4, which simplifies to 3:2.