Question : A boar racer can row $21 \frac{3}{2}$ km/h in still water. If the speed of the river is 12.5 km/hr, it takes him 40 minutes to row to a place and back, how far off is the place (consider up to two decimals)?
Option 1: $5 \frac{5}{27}$ km
Option 2: $5 \frac{2}{5}$ km
Option 3: $4 \frac{5}{27}$ km
Option 4: $3 \frac{5}{27}$ km
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Correct Answer: $5 \frac{5}{27}$ km
Solution :
A boat racer can row $21\frac{3}{2}$ km/h in still water.
The speed of the river is 12.5 km/hr, it takes him 40 minutes to row to a place and back.
Let the distance be $x$, then,
Upstream speed = $21\frac{3}{2}$ km/h - 12.5 km/h
= 22.5 - 12.5
= 10 km/h
Downstream speed = 22.5 km/h + 12.5 km/h
= 35 km/h
According to the question,
$\frac{x}{10} + \frac{x}{35} = \frac{40}{60}$
⇒ $x(\frac{1}{10} + \frac{1}{35}) = \frac{2}{3}$
⇒ $x(\frac{45}{350}) = \frac{2}{3}$
⇒ $x = 2 × \frac{70}{3×9} $
⇒ $x = 5\frac{5}{27}$ km
Hence, The correct answer is $5\frac{5}{27}$ km.
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