Question : A man can row 10 km/hr in still water. When the river is running at a speed of 4.5 km/hr, then it takes him 2 hours to row to a place and comes back to the initial point. How far is the place (in km) (rounded off to two decimal places)?
Option 1: 5.50
Option 2: 8.98
Option 3: 7.98
Option 4: 6.25
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Correct Answer: 7.98
Solution : Downstream speed = (10 + 4.5) = 14.5 km/hr Upstream speed = (10 – 4.5) = 5.5 km/hr Let the distance be $x$ km. According to the question, $\frac{x}{14.5}+\frac{x}{5.5}=2$ ⇒ $\frac{10x}{145}+\frac{10x}{55}=2$ ⇒ $550x+1450x=2×145×55$ ⇒ $2000x=2×145×55$ ⇒ $x=\frac{2×145×55}{2000}$ ⇒ $x= 7.975 \approx 7.98$ km Hence, the correct answer is 7.98.
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