Subject: General Aptitude · Chapter: Boats and Streams · Exam: 2005 · Marks: · Difficulty:
$\mathrm{P}, \mathrm{Q}$ and R are three towns on a river which flows uniformly. Q is equidistant from P and R. I row from P to Q and back in 10 hours and I can row from P to R in 4 hours. Compare the speed of my boat in still water with that of the river.
(a)4 : 3
(b)5 : 3
(c)6 : 5
(d)7 : 3
Answer
Answer (as printed): B
Explanation
Let $P Q=Q R=x \mathrm{km}$. Let speed downstream $=a \mathrm{km} / \mathrm{hr}$, and speed upstream $=b \mathrm{km} / \mathrm{hr}$. Then, $\frac{x}{a}+\frac{x}{b}=10 \Rightarrow x=\frac{10 a b}{a+b}$ And, $\frac{2 x}{a}=4 \Rightarrow x=\frac{4 a}{2}=2 a$ From (i) and (ii), we have : $$2 a=\frac{10 a b}{a+b} \Rightarrow 5 b=a+b \Rightarrow a=4 b . \begin{aligned} \therefore \text { Required ratio } & =\frac{\text { Speed in still water }}{\text { Speed of river }} \\ & =\frac{\frac{1}{2}(a+b)}{\frac{1}{2}(a-b)}=\frac{(a+b)}{(a-b)}=\frac{4 b+b}{4 b-b}=\frac{5}{3} . \end{aligned}$$