Subject: General Aptitude · Chapter: Problems on Trains · Exam: · Marks: · Difficulty:
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
(a)400 m
(b)450 m
(c)560 m
(d)600 m
Answer
Answer (as printed): A
Explanation
Let the length of the first train be $x$ metres. Then, the length of second train is $\left(\frac{x}{2}\right)$ metres. $$\begin{aligned} & \text { Relative speed }=(48+42) \mathrm{kmph} \\ & \qquad=\left(90 \times \frac{5}{18}\right) \mathrm{m} / \mathrm{sec}=25 \mathrm{m} / \mathrm{sec} . \\ & \therefore \frac{\left(x+\frac{x}{2}\right)}{25}=12 \text { or } \frac{3 x}{2}=300 \text { or } x=200 . \\ & \therefore \text { Length of first train }=200 \mathrm{m} . \\ & \text { Let the length of platform be } y \text { metres. } \\ & \text { Speed of the first train }=\left(48 \times \frac{5}{18}\right) \mathrm{m} / \mathrm{sec}=\frac{40}{3} \mathrm{m} / \mathrm{sec} . \\ & \therefore(200+y) \times \frac{3}{40}=45 \\ & \Leftrightarrow 600+3 y=1800 \Leftrightarrow y=400 \mathrm{m} . \end{aligned}$$