Miscellaneous Question 9
- The speed of the boat in still water is $24 $ $kmph$ and the speed of the stream is $4 $ $km / h$. The time is 14 hours taken by the boat to travel from A to $B$ downstream is 36 minutes less than the time taken by the same boat to travel from B to C upstream. If the distance between $A$ and $B$ is $4 km$ more than the distance between $B$ and $C$, what is the distance between $A$ and $B$ ?
(1) $112$ $ km$
(2) $140 $ $km$
(3) $56 $ $km$
(4) $84$ $ km$
(5) $28$ $ km$
(IBPS RRBs Officer Scale-I & II CWE 12.09.2015)
Show Answer
Correct Answer: 9. (3)
Solution: 9. (3) Rate downstream $=24+4=28 \mathrm{kmph}$
Rate upstream $=24-4=20$ $ \mathrm{kmph}$
Distance between A and B $=x $ $\mathrm{km}$.
$\therefore \mathrm{BC}=(x-4) \mathrm{km}$.
According to the question,
$ \begin{aligned} & \frac{x-4}{20}-\frac{x}{28}=\frac{36}{60} \\ & \Rightarrow \frac{7 x-28-5 x}{140}=\frac{3}{5} \\ & \Rightarrow \frac{2 x-28}{140}=\frac{3}{5} \end{aligned} $
$\Rightarrow 2 x-28=\frac{3}{5} \times 140=84$
$\Rightarrow 2 x=84+28=112$
$\Rightarrow x=\frac{112}{2}=56 $ $\mathrm{km}$.
BETA
