| The speed of the current is 5 km/h. A motorboat goes 10 km upstream and back again to the starting point in 50 min. The speed of motorboat in still water is |
A) 20 km/h
B) 26 km/h
C) 28 km/h
D) 25 km/h
Correct Answer: D
Solution :
| Let speed of boat be x km/h. |
| \[\therefore \] Upstream speed of boat \[=(x-5)\,km/h\] |
| Downstream speed of boat \[=(x+5)\] |
| \[\frac{10}{x-5}+\frac{10}{x+5}=\frac{50}{60}\] |
| \[\Rightarrow \] \[10\left( \frac{x+5+x-5}{{{x}^{2}}-{{5}^{2}}} \right)=\frac{50}{60}\] |
| \[\Rightarrow \] \[6\times 2\times 2x={{x}^{2}}-25\] |
| \[\Rightarrow \] \[{{x}^{2}}-25-24x=0\] |
| \[\Rightarrow \] \[{{x}^{2}}+25x+x-25=0\] |
| \[\Rightarrow \] \[(x-25)(x+1)=0\] |
| \[\Rightarrow \] \[x=25\,km/h\] |
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