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CMC Medical CMC-Medical VELLORE Solved Paper-2013

  • question_answer
    In a stream running at 2 km/h, a motorboat goes 6 km upstream and back again to the starting point in 33 min. Find the speed of the motorboat in still water.

    A)  11 km/h             

    B)  22 km/h

    C)  12 km/h             

    D)  20 km/h

    Correct Answer: B

    Solution :

                    Let the speed of the motorboat in still water be x km/h. Then, speed downstream = (x + 2) km / h, Speed upstream = (x - 2) km / h \[\frac{6}{x+2}+\frac{6}{x-2}=\frac{33}{60}\] \[\Rightarrow \]               \[11{{x}^{2}}-240\,x-44=0\] \[\Rightarrow \]               \[11{{x}^{2}}-242\,x+2x-44=0\] \[\Rightarrow \]               \[(x-22)\,(11x+2)=0\] \[\Rightarrow \]               \[x=22\] Hence, speed of motorboat in still water = 22 km/h.


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