Correct Answer: 100. (1)

Solution: 100. (1) Suppose, distance $=d $ $\mathrm{km}$.

$\therefore$ Rate downstream $=x$

$=\frac{d}{5}$ $ \mathrm{kmph}$

Rate upstream $=y=\frac{3 d}{7 \times 3}$

$=\frac{d}{7} $ $\mathrm{kmph}$

$\therefore$ Speed of boat in still water

$=\frac{1}{2}(x+y)$ $ \mathrm{kmph}$

$=\frac{1}{2}\left(\frac{d}{5}+\frac{d}{7}\right)$ $ \mathrm{kmph}$

$=\frac{1}{2}\left(\frac{7 d+5 d}{35}\right) $ $\mathrm{kmph}$

$=\frac{6 d}{35}$ $ \mathrm{kmph}$

Speed of current $=\frac{1}{2}(x-y)$

$=\frac{1}{2}\left(\frac{d}{5}-\frac{d}{7}\right)$ $ \mathrm{kmph}$

$=\frac{1}{2}\left(\frac{7 d-5 d}{35}\right)$ $ \mathrm{kmph}$

$=\frac{d}{35} $ $\mathrm{kmph}$

$\therefore$ Required ratio

$=\frac{6 d}{35}: \frac{d}{35}=6: 1$