Question : A man rows from A to B (upstream) and B to A (downstream) in 12 hours. The distance between A and B is 240 km. The time taken by the man to row 6 km downstream is identical to the time taken by him to row 4 km upstream. What is the speed of the stream?
Option 1: $\frac{35}{3}$ km/hr
Option 2: $\frac{25}{3}$ km/hr
Option 3: $\frac{46}{3}$ km/hr
Option 4: $\frac{50}{3}$ km/hr
Correct Answer: $\frac{25}{3}$ km/hr
Solution :
Let $x$ km/hr be the speed of the still water and $y$ km/hr be the speed of the stream.
The total distance travelled from point A to point B is 240 km, and the total time taken is 12 hours from point A to point B.
Speed upstream = $x - y$, while speed downstream = $x + y$
According to the question,
$\frac{240}{x+y}+\frac{240}{x-y}=12$
⇒ $\frac{1}{x+y}+\frac{1}{x-y}=\frac{1}{20}$
⇒ $\frac{2x}{(x+y)({x-y})}=\frac{1}{20}$
⇒ $({x+y})({x-y})=40x$
⇒ $({x-y})=\frac{40x}{x+y}$ -------------------(1)
According to the question,
$\frac{6}{x+y}=\frac{4}{x-y}$
⇒ $\frac{x+y}{x-y}=\frac{3}{2}$
⇒ $2x+2y=3x-3y$
⇒ $x=5y$
Substitute the value of $x$ in the equation (1),
⇒ $({5y-y})=\frac{40\times 5y}{5y+y}$
⇒ $4y=\frac{200y}{6y}$
⇒ $y=\frac{25}{3}$ km/hr
Hence, the correct answer is $\frac{25}{3}$ km/hr.
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