Subject: General Aptitude · Chapter: Problems on Trains · Exam: · Marks: · Difficulty:
If a train takes 1.75 sec to cross a telegraphic post and 1.5 sec to overtake a cyclist racing along a road parallel to the track @ 10 metres per second, then the length of the train is
(a)105 m
(b)115 m
(c)125 m
(d)135 m
Answer
Answer (as printed): A
Explanation
Let the length of the train be $x$ metres and its speed be $y \mathrm{m} / \mathrm{sec}$. $$\begin{aligned} & \text { Then, } \frac{x}{y}=1.75 \\ & \Leftrightarrow x=1.75 \mathrm{y} . \end{aligned}$$ Since the train takes less time to pass a moving object than a stationary object, it means that the cyclist is moving in a direction opposite to that of the train. $$\begin{aligned} & \therefore \frac{x}{y+10}=1.5 \\ & \Leftrightarrow x=1.5 y+15 \\ & \Leftrightarrow 1.75 y=1.5 y+15 \\ & \Leftrightarrow 0.25 y=15 \Leftrightarrow y=\frac{15}{0.25}=60 . \end{aligned}$$ Length of the train $=1.75 y=(1.75 \times 60) \mathrm{m}=105 \mathrm{m}$.