| In a stream running at 2 km/h, a motorboat goes 5 km upstream and back again to the starting point in 1 h 20 min. Find the speed of the motorboat in still water. |
A) 4 km/h
B) 8 km/h
C) 10 km/h
D) 6 km/h
Correct Answer: B
Solution :
| Let the speed of the motorboat in still water be |
| \[x=km/h.\] |
| Downstream speed \[=(x+2)km/h\] |
| Upstream speed \[=(x-2)\,\,km/h\] |
| \[\therefore \]\[\frac{5}{x+2}+\frac{5}{x-2}=\frac{4}{3}\] |
| \[\Rightarrow \]\[\frac{1}{x+2}+\frac{1}{x-2}=\frac{4}{3}\] |
| \[\Rightarrow \] \[\frac{2x}{{{x}^{2}}-4}=\frac{4}{15}\] |
| \[\Rightarrow \] \[4{{x}^{2}}-16=30x\] |
| \[\Rightarrow \] \[4{{x}^{2}}-30x-16=0\] |
| \[\Rightarrow \] \[2{{x}^{2}}-15x-8=0\] |
| \[\Rightarrow \]\[2x\,\,(x-8)+1\,\,(x-8)=0\] |
| \[\Rightarrow \] \[(x-8)(2x+1)=0\] |
| \[x=8\,\,km/h\] |
| Hence, speed of motorboat in still water is \[8km/h.\] |
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