2 trains running in opposite directions cross a stationary lady standing at a point named F in 26 seconds and 21 seconds respectively. Further, the 2 trains cross each other in 24 seconds. Determine the ratio of the speed of the 2 trains?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3:2
A train passing a person standing still covers its own length, so its length is speed × time. Two trains running in opposite directions pass each other at the sum of their speeds and together cover the sum of their lengths.
The lengths of the trains (each train passes the lady in the time it takes to cover its own length):
Let the speeds be \(x\) and \(y\) (in m/s)
Length of the first train \(=26x\)
Length of the second \(=21y\)
Crossing each other (the sum of the lengths is covered at the sum of the speeds in 24 s):
\(26x+21y=24(x+y)\)
\(26x-24x=24y-21y\), so \(2x=3y\)
\(x:y=3:2\)
Shortcut: If two trains pass a standing person in \(t_1\) and \(t_2\) seconds and pass each other in \(t\) seconds, their speeds are in the ratio \((t-t_2):(t_1-t)\).
\((24-21):(26-24)=3:2\)