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:

Given Data

• Train 1 crosses a standing man in 27 s
• Train 2 crosses a standing man in 17 s
• They cross each other in 23 s
• Required: ratio of their speeds

Step 1: Express lengths via man-crossing times
l₁ = v₁ × 27l₂ = v₂ × 17

Step 2: Use crossing-each-other time
(l₁ + l₂) ÷ (v₁ + v₂) = 23(27v₁ + 17v₂) = 23(v₁ + v₂)v₁(27 − 23) = v₂(23 − 17) ⇒ 4v₁ = 6v₂v₁ : v₂ = 6 : 4 = 3 : 2

Checks & Common Pitfalls

• Do not invert the ratio; keep 3:2 based on the algebra.
• Crossing a man gives length = speed × time.

Final Answer
The ratio of their speeds is 3:2.