The ratio of upstream speed to downstream speed of a boat is $11:14$. If it covers $12$ km upstream and $28$ km downstream in $2$ hours, the stream speed is what percent of the downstream speed?

Question

The ratio of upstream speed to downstream speed of a boat is $11:14$. If it covers $12$ km upstream and $28$ km downstream in $2$ hours, the stream speed is what percent of the downstream speed?

Option A

$9\%$

Option B — Correct answer

$10\frac57\%$

Correct choice.

Option C

$12\%$

Option D

$13\%$

Explanation

Let speeds be $11x$ and $14x$. Then $\frac{12}{11x}+\frac{28}{14x}=2$, so $\frac{12}{11x}+\frac{2}{x}=2$. Solving gives $x=1$. Stream speed $=\frac{14-11}{2}=1.5$ and downstream speed $=14$, so percentage $=\frac{1.5}{14}\times100=10\frac57\%$.

Chapter Mock 9: Boat and Stream