Miscellaneous Question 20
- The ratio between speed of a boat downstream and speed of the boat upstream is $7: 5$ respectively. If the boat travels a distance of $63$ $ km$ downstream in 3 hours, what is the speed of the boat in still water? (in $km / h$ )
20
16
14
12
18
(Bank of Maharashtra PO Exam, 26.10.2016)
Show Answer
Correct Answer: 20. (5)
Solution: 20. (5) Speed of boat in still water $=$ $x$ kmph (let)
Speed of current $=y $ $\mathrm{kmph}$
$\therefore$ Rate upstream
$=(x+y)\ \mathrm{kmph}$
Rate upstream $=(x-y)$ $ \mathrm{kmph}$.
According to the question,
$\frac{x+y}{x-y}=\frac{7}{5}$
By componendo and dividendo,
$\frac{2 x}{2 y}=\frac{7+5}{7-5}$
$\Rightarrow \frac{x}{y}=\frac{12}{2}=6$
$\Rightarrow x=6 y \ldots$ (i)
Again,
$x+y=\frac{63}{3}=21$
$\Rightarrow 7 y=21$
$\Rightarrow y=\frac{21}{7}=3 $ $\mathrm{m/s}$
$\Rightarrow x=6 \times 3=18 $ $\mathrm{kmph}$
BETA
