Two trains of equal length, travelling in opposite directions at 78 km/hr and 117 km/hr, cross each other in 12 seconds. In how much time (in seconds) will the first train cross a platform 455 m long?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 36
Trains running in opposite directions cross at the sum of their speeds and together cover both their lengths. A train crossing a platform covers its own length plus the platform.
Relative speed \(=78+117=195\) km/hr \(\displaystyle =195\times\frac{5}{18}=\frac{325}{6}\) m/s
Sum of lengths \(\displaystyle =\frac{325}{6}\times12=650\) m, so each train is \(325\) m long
Speed of the first train \(\displaystyle =78\times\frac{5}{18}=\frac{65}{3}\) m/s
Distance to cross the platform \(=325+455=780\) m
Time \(\displaystyle =780\div\frac{65}{3}=\frac{780\times3}{65}=36\) s