Miscellaneous Question 23
- A boat takes a total time of twelve hours to travel $105$ $ kms$ upstream and the same distance downstream. The speed of the boat in still water is six times of the speed of the current. What is the speed of the boat in still water? (in $km / hr$ )
(1) 12
(2) 30
(3) 18
(4) 24
(5) 36
Show Answer
Correct Answer: 23. (3)
Solution: 23. (3) Let the speed of current be $x $ $\mathrm{kmph}$.
$\therefore$ Speed of boat in still water $=$ $6 x $ $\mathrm{kmph}$.
$\therefore$ Rate downstream of boat
$=6 x+x=7 x $ $\mathrm{kmph}$.
Rate upstream
$=6 x-x=5 x $ $\mathrm{kmph}$.
According to the question,
$\frac{105}{7 x}+\frac{105}{5 x}=12$
$\Rightarrow \frac{15}{x}+\frac{21}{x}=12$
$\Rightarrow \frac{36}{x}=12 \Rightarrow 12 x=36$ $\Rightarrow x=\frac{36}{12}=3$
$\therefore$ Speed of boat in still water $=6 \times 3=18 $ $\mathrm{kmph}$.
BETA
