Question
Train 'M' can cross a pole in 10 seconds and a 200 metres
long bridge in 15 seconds. Train 'N' whose length is 50% of the length of train 'M' runs in the same direction of train 'M'. If train 'N' crosses train 'M' in 15 seconds, then find the speed of train 'N'.Solution
Let the length and the speed of the train 'M' be 'x' metres and 's' m/s.
ATQ,
(x/s) = 10
So, 'x' = 10s.........(i)
Also, {(x + 200) ÷ s} = 15
Or, 10s + 200 = 15s [from equation (i)]
Or, 200 = (15s - 10s)
Or, 's' = (200/5) = 40
Length of train 'M' = (10 × 40) = 400 metres
So, length of train 'N' = (400 × 0.50) = 200 metres
Let the speed of train 'N' be 'n' m/s.
ATQ,
(400 + 200) ÷ (n - 40) = 15
Or, 600 = 15 × (n - 40)
Or, (n - 40) = 40
So, 'n' = 40 + 40 = 80
Therefore, speed of train 'N' = 80 m/s
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