A) 21 km/h
B) 18 km/h
C) 15 km/h
D) 22 km/h
Correct Answer: D
Solution :
Let the speed of the motorboat in still water be x km/h. Speed downstream \[(x+2)\]km/h, speed upstream\[=(x-2)\] km /h. \[\therefore \]\[\frac{10}{(x-2)}+\frac{10}{(x+2)}=\frac{55}{60}\] \[\Rightarrow \]\[\frac{1}{(x-2)}+\frac{1}{(x+2)}=\frac{55}{600}=\frac{11}{120}\] \[\Rightarrow \]\[\frac{(x+2)+(x-2)}{({{x}^{2}}-4)}=\frac{11}{120}\]\[\Rightarrow \]\[11\,\,({{x}^{2}}-4)=240x\] \[\Rightarrow \] \[11{{x}^{2}}-240x-44=0\] \[\Rightarrow \] \[11{{x}^{2}}-242x+2x-44=0\] \[\Rightarrow \] \[11x\,\,(x-22)+2(x-22)=0\] \[\Rightarrow \] \[(x-22)(11x+2)=0\]\[\Rightarrow \]\[x=22\] Speed of motorboat in still water = 22 km/h
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