Subject: General Aptitude · Chapter: Time and Distance · Exam: 2009 · Marks: · Difficulty:
A train covers a distance between two stations $A$ and $B$ in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations $A$ and $B$ is
(a)55 km
(b)60 km
(c)64 km
(d)80 km
Answer
Answer (as printed): B
Explanation
Let the distance between the stations $A$ and $B$ be $x \mathrm{km}$. Time taken $=45 \mathrm{min}=\frac{3}{4} \mathrm{hr}$. $$\text { ∴ } \text { Original speed }=\left(x \times \frac{4}{3}\right) \mathrm{km} / \mathrm{hr}=\frac{4 x}{3} \mathrm{km} / \mathrm{hr} .$$ New speed $=\left(\frac{4 x}{3}-5\right) \mathrm{km} / \mathrm{hr}=\left(\frac{4 x-15}{3}\right) \mathrm{km} / \mathrm{hr}$. $$\begin{aligned} & \therefore \quad \frac{x}{\left(\frac{4 x-15}{3}\right)}=\frac{48}{60} \Rightarrow \frac{3 x}{4 x-15}=\frac{4}{5} \\ & \Rightarrow 15 x=16 x-60 \Rightarrow x=60 . \end{aligned}$$