A man can row $9 \frac{1}{3}$ kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The speed of the current is :

### Concept & Time-Speed Inversely Proportional For a constant distance, speed and time are inversely proportional. If upstream time is $n$ times downstream time, then downstream speed is $n$ times upstream speed. ### Step-by-Step Solution * **Given:** Boat speed in still water ($B$) = $9 \frac{1}{3} = \frac{28}{3}$ kmph. Upstream Time = $3 \times$ Downstream Time. * Since time is thrice, Upstream speed is one-third of Downstream speed: Downstream Speed ($D$) = $3 \times$ Upstream Speed ($U$) $B + S = 3(B - S)$ * Expand and solve for the ratio of $B$ and $S$: $B + S = 3B - 3S$ $4S = 2B \implies 2S = B \implies S = \frac{B}{2}$ * Substitute the value of $B$ to find Stream speed ($S$): $S = \frac{28/3}{2} = \frac{14}{3} = 4 \frac{2}{3}$ km/hr. ### Exam Strategy & Shortcut Memorize the relationship: If upstream time is $n$ times downstream time, the ratio of boat speed to stream speed is $\frac{n+1}{n-1}$. Here, $n=3$, so $\frac{B}{S} = \frac{3+1}{3-1} = \frac{4}{2} = 2$. $S = \frac{B}{2} = \frac{28/3}{2} = 4 \frac{2}{3}$ km/hr. ### Common Pitfall Setting up the algebraic equation backwards as $U = 3D$, which defies the fundamental logic that moving against the current is always slower. ### Final Answer Therefore, the correct answer is **$4 \frac{2}{3}$ km/hr**.