Each of the questions given below consists of three statements, numbered I, II and II respectively. Please read the question and the statements carefully and decide which of the statement(s) is/are necessary to answer the question.

1)

What is the length of the train $X$ ?

I. Train $X$ crosses a telegraph post in $20$ seconds.

II. Train $X$ crosses a platform of length $800$ m in $100$ seconds.

III. Train $X$ passess through a tunnel $400$ m long in $60$ seconds.

A) I and either II or III only

B) II and III only

C) II and either I or III only

D) III and either I or II only

E) Any two of the three

Option E

### Explanation:

Time taken to cross a pole = Length pf train / Its speed $\Rightarrow 20$ $=\frac{l}{speed}$

$\Rightarrow$ speed $=\frac{l}{20}$ ---(1)

Time taken to cross a platform $=\frac{l+800}{speed}$

$\Rightarrow 100$ $=\frac{l+800}{speed}$ $\Rightarrow$ speed $=\frac{l+800}{100}$ ---(2)

Time taken to pass through a tunnel $=\frac{(l+400)}{60}$

$\Rightarrow 60$ $=\frac{l+400}{speed}$

$\Rightarrow$ speed $=\frac{l+400}{60}$ ---(3)

Equating any two out of three will give us $l$.

$\therefore$ Correct answer is (E).