Subject: General Aptitude · Chapter: Boats and Streams · Exam: 2008 · Marks: · Difficulty:
A motor boat can travel at 10 km/hr in still water. It travelled 91 km downstream in a river a then returned taking altogether 20 hours. Find the rate of flow of the river.
(a)3 km/hr
(b)5 km/hr
(c)6 km/hr
(d)8 km/hr
Answer
Answer (as printed): A
Explanation
Let the rate of flow of the river be $x \mathrm{km} / \mathrm{hr}$. Then, Speed downstream $=(10+x) \mathrm{km} / \mathrm{hr}$; Speed upstream $=(10-x) \mathrm{km} / \mathrm{hr}$ $$\begin{gathered} \therefore \quad \frac{91}{(10+x)}+\frac{91}{(10-x)}=20 \Rightarrow 91\left[\frac{20}{(10+x)(10-x)}\right]=20 \\ \Rightarrow(10+x)(10-x)=91 \\ \Rightarrow 100-x^{2}=91 \Rightarrow x^{2}=9 \Rightarrow x=3 \end{gathered}$$ Hence, rate of flow of the river $=3 \mathrm{km} / \mathrm{hr}$.