Subject: General Aptitude · Chapter: Problems on Trains · Exam: · Marks: · Difficulty:
What is the speed of the train? (S.B.I.P.O., 2002) 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
Answer (as printed): A
Explanation
Let the speed of the train be $x$ metres / sec. Time taken to cross a tree $=\frac{\text { Length of the train }}{\text { Speed of the train }}$. Time taken to cross a platform $$=\frac{(\text { Length of train }+ \text { Length of platform })}{\text { Speed of the train }}$$ I gives, $13=\frac{1}{x} \Rightarrow l=13 x$. II gives, 27 $$\begin{aligned} & =\frac{l+250}{x} \Rightarrow \frac{13 x+250}{x}=24 \\ \Rightarrow & x=\frac{125}{7} \mathrm{m} / \mathrm{sec} . \end{aligned}$$ Thus I and II give the speed of the train. ∴ The correct answer is (a).