Question

Two trains running in opposite directions pass by a man standing on the platform in 20 seconds and 10 seconds respectively and they completely cross each other in 15 seconds. The ratio of their speeds is:

• A. 1:3
• B. 1:2
• C. 1:1.5
• D. 1:1

Hint:

If the crossing time (15s) is exactly the average of the individual times (20s and 10s), the speeds must be equal.

Answer 1

The Correct Option is D

Step 1: Concept
Distance = Speed $\times$ Time. Let speeds be $x$ and $y$. Lengths are $L_1 = 20x$ and $L_2 = 10y$.

Step 2: Meaning
In opposite directions, relative speed is $(x + y)$. Time to cross each other = (Total Length) (Relative Speed).

Step 3: Analysis
$15 = (20x + 10y) / (x + y) \Rightarrow 15x + 15y = 20x + 10y$. Rearranging gives $5y = 5x$.

Step 4: Conclusion
$x/y = 1/1$. The ratio of their speeds is 1:1. Final Answer: (D)