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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