Miscellaneous Question 40
- At $10 \%$ lesser (than usual) speed (in still water), a boat covers 110 $km$ downstream in 5 hours. If the boat’s usual speed (in still water) is $400 \%$ more than the stream’s speed, in what time will it cover $120$ $ km$ upstream at its usual speed?
(1) 6 hours
(2) 7 hours 30 minutes
(3) 8 hours
(4) 8 hours 30 minutes
(5) 9 hours
(Canara Bank PO Exam 04.03.2018)
Show Answer
Correct Answer: 40. (2)
Solution:
- (2) Speed of current $=x $ $\mathrm{kmph}$.
$\therefore$ Speed of boat in still water $=5 x $ $\mathrm{kmph}$.
Its speed in still water is reduced by $10 \%$.
$\therefore$ Rate downstream
$=5 \times \frac{9 x}{10}+x$
$=\frac{9 x}{2}+x=\frac{11 x}{2} $ $\mathrm{kmph}$.
According to the question,
$\frac{110}{\frac{11 x}{2}}=5$ $\Rightarrow \frac{110 \times 2}{11 x}=5$
$\Rightarrow x=\frac{20}{5}=4 $ $\mathrm{kmph}$.
$\therefore$ Rate upstream of boat
$=5 x-x=4 x $ $\mathrm{kmph}$.
$=4 \times 4=16 $ $\mathrm{kmph}$.
$\therefore$ Required time $=\frac{120}{16}$
$=7 \frac{1}{2}$ hours
$=7$ hours 30 minutes
BETA
