Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

Given Data

• Two trains start simultaneously from opposite stations (Howrah ↔ Patna)
• After meeting, they reach destinations in 9 h and 16 h respectively
• Required: ratio of their speeds

Step 1: Key relation after meeting
If times taken after meeting are t₁ and t₂, thent₁/t₂ = (v₂/v₁)²⇒ v₁/v₂ = √(t₂/t₁)

Step 2: Substitute values
t₁ = 9 h, t₂ = 16 hv₁:v₂ = √(16/9) = 4:3

Checks & Common Pitfalls

• Speeds are in the inverse ratio of the square roots of times after meeting.
• Do not use simple inverse times (that would give 9:16, which is incorrect).

Final Answer
The ratio of their speeds is 4:3.