| In a stream running at 5 km/h, a motorboat goes 1 km upstream and back again to the starting point in 35 min. Find the speed of the motorboat in still water. |
A) 12 km/h
B) 5 km/h
C) 7 km/h
D) 14 km/h
Correct Answer: C
Solution :
| Let the speed of the motorboat in still water be x km/h. |
| Downstream speed \[=(x+5)km/h\] |
| Upstream speed \[=(x-5)km/h\] |
| \[\therefore \] \[\frac{1}{x+5}+\frac{1}{x-5}=\frac{35}{60}\] |
| \[\Rightarrow \] \[\frac{2x}{{{x}^{2}}-25}=\frac{7}{12}\] |
| \[\Rightarrow \] \[7\,\,({{x}^{2}}-25)=24x\] |
| \[\Rightarrow \] \[7{{x}^{2}}-24x-175=0\] |
| \[\Rightarrow \]\[7x\,\,(x-7)+24\,\,(x-7)=0\] |
| \[\Rightarrow \] \[(x-7)(7x+24)=0\] |
| \[x=7\] |
| Thus, speed of the motorboat in still water \[=7km/h\] |
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