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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