Miscellaneous Question 25
- A boat takes a total time of eight hours to travel $63$ $ kms$ upstream and the same distance downstream. The speed of the current is $\frac{1}{8}$ th of the speed of the boat in still water. What is the speed of the boat in still water? (in km/ hr)
(1) 32
(2) 24
(3) 16
(4) 8
(5) 36
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Correct Answer: 25. (3)
Solution: 25. (3) Speed of boat in still water $=$ $8 x$ $ \mathrm{kmph}$. (let)
$\therefore$ Speed of current $=x $ $\mathrm{kmph}$.
$\therefore$ Rate downstream
$=(8 x+x) $ $\mathrm{kmph}$.
$=9 x $ $\mathrm{kmph}$.
Rate upstream $=7 x $ $\mathrm{kmph}$.
$\because$ Time $=\frac{\text { Distance }}{\text { Speed }}$
$\therefore \frac{63}{9 x}+\frac{63}{7 x}=8$
$\Rightarrow \frac{7}{x}+\frac{9}{x}=8$
$\Rightarrow \frac{16}{x}=8$
$\Rightarrow x=\frac{16}{8}=2$
$\therefore$ Speed of boat in still water $=$ $8 x=16 $ $\mathrm{kmph}$.
BETA
