Question

A train crosses another train which is running in the opposite direction in `t' seconds. What is the speed of the train?

I. Both the trains are running at the same speed and have the same length.

II. One of the trains cross a pole in 10 seconds.

• 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 D

if the data even in both Statements I and II together are not sufficient 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 $=\frac{\left(x+y\right)}{\left(u+v\right)}m/sec.\Rightarrow t=\frac{\left(x+x\right)}{\left(u+u\right)}=\frac{x}{u}.....\left(i\right)$

Time taken to cross the pole $=\frac{Lengthofthetrain}{Speedofthetrain}=\frac{x}{u}\Rightarrow \frac{x}{u}=10.....\left(ii\right)$

From (i) and (ii) also, we cannot find `u'.