A 240 m long train crosses a platform of equal length in 27 s. What is the speed of the train in km/h?

We know that,
Speed = Distance/ Time
Speed of the train = 220/12 x (18/5) km/h

We know that, the distance covered by a train in passing a pole or a standing man or a signal post or any other object (of negligible length) is equal to the length of the train.

In this case, train covers 90 m to cross a standing man.
? Length of the train = 90 m

Distance covered by train in 10 sec = (50 + 100) = 150 m
? Speed = 150/10 m/sec = 15 x (18/5) = 54 km/hr

Distance covered in 2/60 hours = (1 + 1/2) = 3/2 km
Distance covered in 1 hour = (3/2) x (60/2) = 45 km
So, speed of the train = 45 km/hr

Total distance = 70 + 80 = 150 m
Relative speed = 68 + 40 = 108 kmph = 108 x (5/18) = 30 m/s
So time taken = 150 / 30 = 5 seconds.

Length of platform is not given. it can not be determined.

When two trains are moving in opposite directions then their relative speed is equal to the sum of the speed of both the trains.
? Required relative speed = 6 + 12 = 18 m/s

We know that, if two trains are running in the same direction, then relative speed is equal to the difference of the speeds of both the trains.
? Required relative speed = 21 - 15 = 6 km/h

Relative speed of train
= Speed of train + Speed of car
? 90 = Speed of train + 15
? Speed of train = 90 - 15 = 75 km/h

Speed of the train = 18 km/h = 18 x 5/18 m/s = 5 m/s
Distance covered = Length of the train = 120 m
? Time taken by the train to cross the man = Distance/Speed
= 120/5 = 24 s