Question

In what time will a train 100 meters long with a speed of \[50\text{ }km/hr\] cross a pillar?
(a) 7 seconds
(b) 72 seconds
(c) 7.2 seconds
(d) 70 seconds

Answer 1

Hint:The train will have to cover 100 meters to cross the pillar. The distance to be covered by the train is 100 meters. The speed of the train is \[50\text{ }km/hr\] . Convert the distance to be covered by the train into kilo-meters using the relation 1 km = 1000 meters. Now, use the formula to get the time, \[\text{Time = }\dfrac{\text{Distance}}{\text{Speed}}\] . Then, convert the time in seconds using the relation 1 hr = 3600 seconds and solve it further.

Complete step-by-step answer:
According to the question, we have a train which is 100 meters long and the train is having a speed of \[50\text{ }km/hr\] .
To cross the pillar the train will have to cover 100 meters.
Now, we have to find the time taken by the train to cover 100 meters.
The distance which is to covered by the train = 100 meters ……………….(1)
The speed of the train = \[50\text{ }km/hr\] …………………..(2)
We know the formula, \[\text{Time = }\dfrac{\text{Distance}}{\text{Speed}}\] ……………..(3)
Here, we cannot apply this formula directly because in equation (1) and equation (2), we can see that the unit of distance is in meters and the unit of speed of the train is in kilo-meters per hour. So, we have to convert the distance in kilo-meters.
We know that, 1 km = 1000 meters ………………(4)
From equation (1) and equation (4), we get
The distance which is to covered by the train = 100 meters = \[\dfrac{100}{1000}km=\dfrac{1}{10}km\] …………….(5)
Now, from equation (2), equation (3) and equation (4), we get
\[\text{Time = }\dfrac{\text{Distance}}{\text{Speed}}\]
\[\text{Time = }\dfrac{\dfrac{1}{10}}{50}=\dfrac{1}{500}hr\] ………………(6)
Now, we have to convert the calculated time into seconds.
We know that, 1 hr = 3600 seconds …………………(7)
From equation (6) and equation (7), we get
\[\text{Time =}\dfrac{\text{1}}{\text{500}}\text{hr=}\dfrac{\text{1}}{\text{500}}\text{ }\!\!\times\!\!\text{ 3600seconds=}\dfrac{\text{3600}}{\text{500}}\text{seconds=7}\text{.2seconds}\] .
Therefore, the time taken by the train to cross the pillar is 7.2 seconds.
Hence, the correct option is option (c).

Note: In this question one might put the distance as 100 and speed as 50 in the formula \[\text{Time = }\dfrac{\text{Distance}}{\text{Speed}}\] . This is wrong. We cannot use this formula directly. First of all, we have to convert the distance which is meters into kilo-meters and then use this formula.