Question : A man can row 12 km/hr in still water. It takes him 4 times as long to row up as to row down the river. The speed of the stream is:
Option 1: 7.2 km/hr
Option 2: 3.6 km/hr
Option 3: 9.8 km/hr
Option 4: 4.9 km/hr
Correct Answer: 7.2 km/hr
Solution :
Let the speed of the stream as $v$ km/hr.
When the man rows downstream (with the current), his effective speed is (12 + $v$) km/hr.
When he rows upstream (against the current), his effective speed is (12 – $v$) km/hr.
Given that it takes him 4 times as long to row upstream as downstream, the distance travelled in both directions is the same,
$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
$⇒\frac{\text{Distance}}{12 - v} = 4 \times \frac{\text{Distance}}{12 + v}$
$⇒\frac{\text{1}}{12 - v} = \frac{\text{4}}{12 + v}$
$⇒12+v = 4(12-v)$
$⇒5v=36$
$⇒v=7.2$
Hence, the correct answer is 7.2 km/hr.
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