Question

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform which is 650 m long?
(a) 65 seconds
(b) 89 seconds
(c) 100 seconds
(d) 150 seconds

Answer 1

Hint: We can find the speed of the train by using the information that a train 240 m long takes 24 seconds to pass a pole. We know the formula for speed as $\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$. Substituting distance and time as 240 and 24 respectively we get the speed. Then a train has to cross a platform of length 650 m so the total distance traversed by the train is the addition of 650 and 240 and speed we have already calculated so substituting this distance and speed in the speed formula we will get the time in which the train crossed the platform.

Complete step by step answer:
We have given a 240 m long train and the time it takes to cross a pole is 24 seconds and we are asked to find the time that the same train will take to cross a 650 m platform.
The distance travelled by the train in crossing the pole is equal to its own length i.e. 240 m so we know the distance and time as 24 seconds we can find the speed of the train using the following formula:
$\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$
Substituting distance as 240 m and time as 24 seconds we get,
$\text{Speed}=\dfrac{240}{24}=10\text{m/s}$
Hence, we got the speed of the train as 10 m/s.
Now, we have to find the time the train takes to cross 650 m long platform in which the total distance that train traversed in crossing the platform is the addition of 650 m and its length (i.e. 240 m) which we have shown below:
Total distance traversed by the train $=650+240=890$
 And speed we have already calculated as 10 m/s
Substituting the value of speed as 10 and distance as 890 in the speed formula we get,
$10=\dfrac{890}{\text{Time}}$
Rearranging the above equation we get,
$\begin{align}
  & Time=\dfrac{890}{10} \\
 & \Rightarrow Time=89\text{seconds} \\
\end{align}$
From the above calculations, the train will take 89 seconds to cross the platform.

So, the correct answer is “Option B”.

Note: The possible mistake that you could make in this problem is that in finding the time taken by the train to cross the platform of 650 m length you forgot to add the length of the train. You might have thought that the train has just travelled 650 m length of the platform but in the question we are asked the time taken by the train to pass the platform of 650 m, to pass the platform the train has to travel an extra length of its own.