Miscellaneous Question 22
- A boat takes six hours to travel a certain distance downstream and five hours to travel a certain distance upstream. The distance travelled upstream is half of the travelled downstream. If the speed of the current is $4$ $ km / hr$, what is the speed of the boat in still water? (in $km / hr$ )
(1) 16
(2) 20
(3) 24
(4) 10
(5) 18
(IBPS RRBs Officer CWE (Pre.) 14.11.2016 (Shift-I))
Show Answer
Correct Answer: 22. (1)
Solution: 22. (1) $x^{3}-19 x+30$
$(x-2)$ is the factor of the above expression.
Because for $x=2$
$ (2)^{3}-19 \times (2)+30=0$
Let speed of boat in still water be $x$ $ \mathrm{kmph}$.
$\therefore$ Rate downstream $=(x+4) $ $\mathrm{kmph}$
Rate upstream $=(x-4) $ $\mathrm{kmph}$
Distance covered downstream in 6 hours $=6(x+4) $ $\mathrm{km}$.
Distance covered upstream in 5 hours $=5(x-4)$ $ \mathrm{km}$.
According to the question,
$2 \times 5(x-4)=6(x+4)$
$\Rightarrow 10 x-40=6 x+24$
$\Rightarrow 10 x-6 x=40+24$
$\Rightarrow 4 x=64$
$\Rightarrow x=\frac{64}{4}=16$ $ \mathrm{kmph}$
BETA
