Subject: General Aptitude · Chapter: Problems on Trains · Exam: 2006 · Marks: · Difficulty:
A train with 90 km/hr crosses a bridge in 36 seconds. Another train 100 metres shorter crosses the same bridge at 45 km/hr. What is the time taken by the second train to cross the bridge?
(a)61 seconds
(b)62 seconds
(c)63 seconds
(d)64 seconds
Answer
Answer (as printed): D
Explanation
Let the lengths of the train and the bridge be $x$ metres and $y$ metres respectively. $$\begin{aligned} & \text { Speed of the first train }=90 \mathrm{km} / \mathrm{hr}=\left(90 \times \frac{5}{18}\right) \mathrm{m} / \mathrm{sec} \\ & \quad=25 \mathrm{m} / \mathrm{sec} \end{aligned}$$ Speed of the second train $=45 \mathrm{km} / \mathrm{hr}$ $$=\left(45 \times \frac{5}{18}\right) \mathrm{m} / \mathrm{sec}=\frac{25}{2} \mathrm{m} / \mathrm{sec} .$$ Then, $\frac{x+y}{36}=25 \Leftrightarrow x+y=900$ ∴ Required time $=\left[\frac{(x-100)+y}{\left(\frac{25}{2}\right)}\right] \sec =\left[\frac{(x+y)-100}{\left(\frac{25}{2}\right)}\right]$ $$\sec =\left(800 \times \frac{2}{25}\right) \sec =64 \mathrm{sec} .$$