Subject: General Aptitude · Chapter: Problems on Trains · Exam: · Marks: · Difficulty:
A train 400 m long overtook a man walking along the line in the same direction as the train, at the rate of 5 kmph and passed him in 40 seconds. The train reached the station in 20 minutes after passing the man. In what time did the man reach the station?
(a)2 hr 24 min
(b)2 hr 30 min 40 sec
(c)2 hr 36 min 48 sec
(d)2 hr 48 min 48 sec
Answer
Answer (as printed): D
Explanation
Speed of the train relative to man $$=\left(\frac{400}{40}\right) \mathrm{m} / \mathrm{sec}=10 \mathrm{m} / \mathrm{sec}=\left(10 \times \frac{18}{5}\right) \mathrm{km} / \mathrm{hr}=36 \mathrm{km} / \mathrm{hr} .$$ Let the speed of the train be $x \mathrm{kmph}$. Then, relative speed $=(x-5) \mathrm{kmph}$. $$\therefore x-5=36 \text { or } x=41 \mathrm{kmph} .$$ Distance covered by the station in 20 min $$=\left(41 \times \frac{20}{60}\right) \mathrm{km}=\frac{41}{3} \mathrm{km} .$$