Correct Answer: 36. (1)

Solution: 36. (1) Speed of current $\left(S_{1}\right)$ $=y$ $ \mathrm{kmph}$

Speed of boat in still water $=x $ $\mathrm{kmph}$.

$\therefore$ Rate downstream

$=x+y=\left(\frac{65}{\frac{13}{2}}\right)$ $ \mathrm{kmph}$

$=\left(\frac{65 \times 2}{13}\right) $ $\mathrm{kmph}$

$=10 $ $\mathrm{kmph}$

Speed of current $\left(\mathrm{S}_{2}\right)$

$=\frac{11 y}{10} $ $\mathrm{kmph}$

$\therefore$ Rate upsteam $=x-\frac{11 y}{10}$

$=5.8 $ $\mathrm{kmph}$

$\therefore x+y-x+\frac{11 y}{10}$

$=(10-5.8)$ $ \mathrm{kmph}$

$\Rightarrow \frac{10 y+11 y}{10}=4.2$

$\Rightarrow \frac{21 y}{10}=4.2 \Rightarrow y=\frac{4.2 \times 10}{21}$

$=2 $ $\mathrm{kmph}$

$\Rightarrow$ Speed of current $\left(\mathrm{S}_{2}\right)$

$=\left(\frac{11 \times 2}{10}\right) $ $\mathrm{kmph}$

$=2.2 $ $\mathrm{kmph}$