Subject: General Aptitude · Chapter: Time and Distance · Exam: · Marks: · Difficulty:
A journey of 192 km between two cities takes 2 hours less by a fast train than by a slow train. If the average speed of the slow train is 16 km/hr less than that of the fast train, then the average speed of the fast train is
(a)32 km/hr
(b)36 km/hr
(c)48 km/hr
(d)64 km/hr
Answer
Answer (as printed): C
Explanation
Let the speed of the fast train be $x \mathrm{km} / \mathrm{hr}$. Then, speed of the slow train $=(x-16) \mathrm{km} / \mathrm{hr}$. $$\begin{aligned} & \therefore \frac{192}{x-16}-\frac{192}{x}=2 \Rightarrow \frac{1}{x-16}-\frac{1}{x}=\frac{1}{96} \\ & \Leftrightarrow x^{2}-16 x-1536=0 \Leftrightarrow(x-48)(x+32)=0 \Leftrightarrow x=48 . \end{aligned}$$