Subject: General Aptitude · Chapter: Boats and Streams · Exam: 2001 · Marks: · Difficulty:
At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12miles. What is the speed of the current in miles per hour?
(a)$1 \frac{1}{3}$
(b)$1 \frac{2}{3}$
(c)$2 \frac{1}{3}$
(d)$2 \frac{2}{3}$
Answer
Answer (as printed): D
Explanation
Let the speed in still water be $x \mathrm{mph}$ and the speed of the current be $y \mathrm{mph}$. Then, Speed upstream $=(x-y)$; Speed downstream $=(x+y)$ $$\begin{aligned} & \therefore \frac{12}{(x-y)}-\frac{12}{(x+y)}=6 \Leftrightarrow 6\left(x^{2}-y^{2}\right)=24 y \\ & \Leftrightarrow x^{2}-y^{2}=4 y \Leftrightarrow x^{2}=\left(4 y+y^{2}\right) \end{aligned}$$ And, $\frac{12}{(2 x-y)}-\frac{12}{(2 x+y)}=1$ $$\Leftrightarrow 4 x^{2}-y^{2}=24 y \Leftrightarrow x^{2}=\frac{24 y+y^{2}}{4}$$ From (i) and (ii), we have : $$\begin{aligned} 4 y+y^{2}=\frac{24 y+y^{2}}{4} & \Leftrightarrow 16 y+4 y^{2}=24 y+y^{2} \\ & \Leftrightarrow 3 y^{2}=8 y \Leftrightarrow y=\frac{8}{3} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.