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.

**Answer:**

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)**.