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A train 200m long passes a pole in 10 seconds. How long will it take to cross a platform 300m long?
20┬аseconds
25┬аseconds
30┬аseconds
15┬аseconds
25┬аseconds
Use the ratio of distances: The train covers 200m in 10s. It covers (200 + 300) = 500m in 20010тАЛ├Ч500=25s.
Length of train = 200m, Time to pass a pole = 10s, Length of platform = 300m.
Speed=TimeDistanceтАЛ, Time=SpeedTotalDistanceтАЛ
Use the ratio of distances: The train covers 200m in 10s. It covers (200 + 300) = 500m in 20010тАЛ├Ч500=25s.
Adding only the platform length (300m) instead of the total distance (train + platform = 500m) is the most common mistake.
Calculate speed of the train
When a train passes a pole, it covers its own length. Using Speed=TimeDistanceтАЛ, we find the speed.
v=10┬аs200┬аmтАЛ=20┬аm/s
Calculate total distance to cover
To cross the platform, the train must cover its own length plus the platform length.
DtotalтАЛ=200┬аm+300┬аm=500┬аm
Calculate time taken
Divide total distance by the constant speed of the train to find the time taken.
t=20┬аm/s500┬аmтАЛ=25┬аs
B is correct because the total distance of 500m covered at a speed of 20m/s results in a time of 25 seconds.
This concept of total distance (Object Length + Obstacle Length) is identical to problems involving trains crossing bridges, tunnels, or other trains.