Question
Train 'X' can cross a pole in 15 seconds and a 180 metres
long bridge in 18 seconds. Train 'Y' whose length is 80% of the length of train 'X' runs in the same direction of train 'X'. If train 'Y' crosses train 'X' in 12 seconds, then find the speed of train 'Y'.Solution
Let the length and the speed of the train 'X' be 'x' metres and 's' m/s.
ATQ,
(x/s) = 15
So, 'x' = 15s.........(i)
Also, {(x + 180) ÷ s} = 18
Or, 15s + 180 = 18s [from equation (i)]
Or, 180 = (18s - 15s)
Or, 's' = (180/3) = 60
Length of train 'X' = (15 × 60) = 900 metres
So, length of train 'Y' = (900 × 0.80) = 720 metres
Let the speed of train 'Y' be 'y' m/s.
ATQ,
(900 + 720) ÷ (y - 60) = 12
Or, 1620 = 12 × (y - 60)
Or, (y - 60) = 135
So, 'y' = 135 + 60 = 195
Therefore, speed of train 'Y' = 195 m/s
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