Question

What is the speed of the train?
I. The train crosses a tree in 13 seconds.
II. The train crosses a platform of length 250 metres in 27 seconds.
III. The train crosses another train running in the same direction in 32 seconds.

• A. I and II only
• B. II and III only
• C. I and III only
• D. Any two of the three
• E. None of these

Answer 1

The correct option is A I and II only

Let the speed of the train be x metres/sec.
Time taken to cross a tree $=\frac{Lengthofthetrain}{\text{Speed of the train}}$
Time taken to cross a platform $=\frac{\text{(Length of the train + Length of the Platform)}}{\text{Speed of the train}}$
I gives, $13=\frac{l}{x}\Rightarrow 13x$
II gives $27=\frac{l+250}{x}$
$\Rightarrow \frac{13x+250}{x}=27$
$\Rightarrow x=\frac{125}{7}m/sec.$
Thus I and II give the speed of the train.
$\therefore$ The correct answer is (A).