Question : A motorboat, whose speed is 20 km/hr in still water takes 3 hours to cover a distance of 22.5 km upstream and then comes back to its starting point. The speed of the stream (in km/hr ) is:
Option 1: 10
Option 2: 9
Option 3: 8
Option 4: 11
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Correct Answer: 10
Solution :
Let, the speed of the water = $x$ km/hr
Speed of motorboat in still water = 20 km/hr
Downstream speed = $(20 + x)$ km/hr
Upstream speed = $(20 - x)$ km/hr
Time taken to go downstream = $\frac{22.5}{(20+x)}$
Time taken to go upstream = $\frac{22.5}{(20-x)}$
According to the question,
$⇒\frac{22.5}{(20+x)} + \frac{22.5}{(20-x)} = 3$
$⇒\frac{22.5(20-x)+22.5(20+x)}{(20+x)(20-x)}=3$
$⇒450-22.5x+450+22.5x = 3(400-x^2)$
$⇒900=1200-3x^2$
$⇒3x^2 = 300$
$⇒x^2 = 100$
$⇒x = 10$ km/hr
Hence, the correct answer is 10.
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