Subject: General Aptitude · Chapter: Time and Distance · Exam: 2010 · Marks: · Difficulty:
The average speed of a train is 20\% less on the return journey than on the onward journey. The train halts for half an hour at the destination station before starting on the return journey. If the total time taken for the to and fro journey is 23 hours, covering a distance of 1000 km, the speed of the train on the return journey is
(a)40 km/hr
(b)50 km/hr
(c)55 km/hr
(d)60 km/hr
Answer
Answer (as printed): A
Explanation
Let the average speed on the onward journey be $x \mathrm{km} / \mathrm{hr}$. Then, average speed on return journey $$\begin{aligned} & =(80 \% \text { of } x) \mathrm{km} / \mathrm{hr}=\left(\frac{4 x}{5}\right) \mathrm{km} / \mathrm{hr} . \\ & \therefore \quad \frac{500}{x}+\frac{500}{\left(\frac{4 x}{5}\right)}+\frac{1}{2}=23 \Rightarrow \frac{500}{x}+\frac{625}{x}=\frac{45}{2} \\ & \Rightarrow \quad \frac{1125}{x}=\frac{45}{2} \Rightarrow x=\frac{1125 \times 2}{45}=50 . \end{aligned}$$ Hence, speed on return journey $$=\left(\frac{4 x}{5}\right)=\left(\frac{4 \times 50}{5}\right) \mathrm{km} / \mathrm{hr}=40 \mathrm{km} / \mathrm{hr} .$$