Correct Answer: 13. (1)

Solution: 13. (1) Speed of boat in still water $=$ $x$ kmph.

Speed of current $=y $ $\mathrm{kmph}$

Rate downstream $=(x+y) $ $\mathrm{kmph}$

Rate upstream $=(x-y)$ $ \mathrm{kmph}$.

According to the question,

$x+y=\frac{20}{1 \frac{40}{60}} \mathrm{kmph}$

$\Rightarrow x+y=\frac{20}{\frac{5}{3}}=\frac{20 \times 3}{5}$

$=12$ $ \mathrm{kmph}$

$\therefore \frac{2 \times 20}{x+y}=\frac{20}{x-y}$

$\Rightarrow 2 x-2 y=x+y$

$\Rightarrow x=3 y$

From equation (i),

$3 y+y=12$

$\Rightarrow 4 y=12 \Rightarrow y=\frac{12}{4}=3 $ $\mathrm{kmph}$

$\therefore x=3 \times 3=9$ $ \mathrm{kmph}$

$\therefore$ Rate upstream

$=(x-y) $ $\mathrm{kmph}$

$=9-3=6 $ $\mathrm{kmph}$