Question

A man can row $7.5$ kmph in still water. If in a river running at $1.5$ kmph, it takes him $50$ minutes to row to a place and back, how far off is the place?

• A. $2$ km
• B. $3.5$ km
• C. $3$ km
• D. $5$ km

Answer 1

The correct option is C $3$ km

Speed downstream $=(7.5+1.5)\text{kmph}=9\text{kmph}$
Speed upstream $=(7.5-1.5)\text{kmph}=6\text{kmph}$
Let the required distance be $x\text{km}.$
Then, $\frac{x}{9}+\frac{x}{6}=\frac{50}{60}$
$\Rightarrow 2x+3x=\frac{5}{6}\times 18\Rightarrow 5x=15$
$\Rightarrow x=3$
Hence, the required distance is $3\text{km}.$