Question

What is the length of a running passenger train crossing another 360 metre long goods train running in the opposite direction?

I. The relative speed of the two trains is 300 kmph.

II. The trains take 18 seconds to cross each other.

• A. if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
• B. if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
• C. if the data either in Statement I or in Statement II alone are sufficient to answer the question.
• D. if the data even in both Statements I and II together are not sufficient to answer the question.
• E. if the data in both Statements I and II together are necessary to answer the question.

Answer 1

The correct option is E

if the data in both Statements I and II together are necessary to answer the question.

Let the two trains of length `x' metres and `y' metres be moving in opposite directions at `u' m/s and `v' m/s.

Time taken to cross each other $=\frac{\left(x+y\right)}{\left(u+v\right)}sec.$

Now, y = 360, u + v $=\left(300\times \frac{5}{18}\right)m/sec=\frac{250}{3}m/sec.$

$\Rightarrow 18=\frac{x+360}{\left(250/3\right)}\Rightarrow x=\left(1500-360\right)=1140m.$

Thus, both I and II are necessary to get the answer.