Question

If a train takes 1 second to cross a telegraph post and 3 seconds to cross 300m long, then, the length of the train in meters is
A. 100
B. 150
C. 200
D. 300

Answer 1

Hint: In this case the time taken for the train to cross two objects are given. The length of the telegraph post can be considered negligible, and the distance travelled by the train to cross it can be considered to be equal to the length of the train. However, the distance travelled by the train to cross the platform should be equal to the length of the platform plus the length of the train. Thereafter, using the speed distance formula, we can calculate the length of the train.

Complete step-by-step answer:

In this question the time taken by the train to cross the telegraph post and the platform is given. Therefore, we shall use the speed-distance formula which states that
$\text{speed=}\dfrac{\text{distance travelled}}{\text{time taken}}..................(1.1)$
Let the length of the train be x meters.
The length of the telegraph post can be considered to be negligible. Thus, the distance travelled by the train to cross the telegraph should be equal to the length of the train which is equal to x. It is given that the time taken to cross it is 1second. Thus, from equation (1.1),
$\text{speed of the train = }\dfrac{x}{1}\text{ m/s}=x\text{ m/s}..................(1.2)$

Also, while crossing the platform, the distance travelled by the train should be equal to the sum of the distance of the train and the platform. The time taken to cross it is given to be 3seconds. Therefore,
$\text{speed of the train=}\dfrac{300+x}{3}\text{ m/s}.............\text{(1}\text{.3)}$
However, the speed of the train in both cases should be the same. Thus, from equation (1.2) and (1.3), we get
$\begin{align}
  & \text{speed of the train}=x\text{ m/s}=\dfrac{300+x}{3}\text{ m/s} \\
 & \Rightarrow \text{x=}\dfrac{300+x}{3}\Rightarrow 3x=300+x\Rightarrow 2x=300 \\
 & \Rightarrow x=150 \\
\end{align}$
Therefore, the length of the train is found to be 150m which matches option (B). Hence, option (B) is the correct answer to this question.

Note: In this case, we should be careful to use the correct units while adding the distances. For example, in equation (1.3), the units of both 300m and x are in meters and the time is in seconds, therefore the addition of the quantities and the unit of speed as m/s is valid. When quantities are given in different units, we should convert them to the same units before adding them.