Train 'R' can cross a pole in 6 seconds and a 240 metres

Solution

Let the length and the speed of the train 'R' be 'x' metres and 's' m/s.
ATQ,
(x/s) = 6
So, 'x' = 6s.........(i)
Also, {(x + 240) ÷ s} = 10
Or, 6s + 240 = 10s [from equation (i)]
Or, 240 = (10s - 6s)
Or, 's' = (240/4) = 60
Length of train 'R' = (6 × 60) = 360 metres
So, length of train 'S' = (360 × 0.75) = 270 metres
Let the speed of train 'S' be 't' m/s.
ATQ,
(360 + 270) ÷ (t - 60) = 14
Or, 630 = 14 × (t - 60)
Or, (t - 60) = 45
So, 't' = 45 + 60 = 105
Therefore, speed of train 'S' = 105 m/s