Question

A boatman rows to a place at a distance of $45$ km and back in $20$ hours. He finds that he can row $12$ km with the stream in the same time as $4$ km against the stream. Find the speed of the stream.

• A. $3$ km/hr
• B. $2.5$ km/hr
• C. $4$ km/hr
• D. $3.5$ km/hr

Answer 1

The correct option is A $3$ km/hr

Ratio of upstream speed to downstream speed $=1:3$
$\therefore$ Ratio of times taken to cover a certain distance upstream and downstream $=3:1$.
Given, the man took $20$ hours to cover the $45$ km distance and back $\Rightarrow$ He took $15$ hours to cover $45$ km upstream and $5$ hours to cover $45$ km downstream.
$\therefore$ Speed of downstream $=$ $\frac{45}{5}=9$ km/hr
Speed of upstream $=$ $\frac{45}{15}=3$ km/hr
$\therefore$ Speed of stream $=$ $\frac{1}{2}(9-3)$ km/hr $=3$ km/hr