Subject: General Aptitude · Chapter: Problems on Trains · Exam: · Marks: · Difficulty:
What is the speed of the train? I. The train passes a man walking at the rate of 3 kmph in 9 seconds. II. The train passes a man walking at the rate of 6 kmph in 10 seconds. III. The train is moving in the same direction in which the two men are moving.
(a)I and III only
(b)II and III only
(c)I and II only
(d)All I, II and III
(e)Question cannot be answered even with infor- mation in all the three statements.
Answer
Answer (as printed): D
Explanation
Let the speed of the train be $x \mathrm{m} / \mathrm{sec}$. III gives that the men are moving in the same direction. I gives, time taken to pass a man $$=\frac{l}{\left(x-3 \times \frac{5}{18}\right)}=\left(\frac{6 l}{6 x-5}\right) \sec .$$ $\begin{array}{ll}\therefore \quad \frac{6 l}{6 x-5} & =9 \Rightarrow 54 x-6 l=45\end{array}$ $\Rightarrow 18 x-2 l=15$ II gives, time taken to pass another man $$=\frac{l}{\left(x-6 \times \frac{5}{18}\right)} \sec =\frac{3 l}{(3 x-5)} \sec .$$ $\therefore \quad \frac{3 l}{(3 x-5)}=10 \Rightarrow 30 x-3 l=50$ On solving (i) and (ii), we get : $x=\frac{55}{6} \mathrm{m} / \mathrm{sec}$. Thus, all I, II, III are needed to get the answer. ∴ (d) is correct.