| A boat goes 12 km downstream and comes back to the starting point in 3 h. If the speed of current is 3 km/h, then the speed (in km/h) of the boat in still water is [SSC (CISF) 2010] |
A) 12
B) 9
C) 8
D) 6
Correct Answer: B
Solution :
| If the speed of boat in still water be \[x\,\,km/h.\] |
| Then, speed in downstream \[=(x+3)km/h\] |
| Speed in upstream \[=(x-3)km/h\] |
| According to the question, |
| \[\frac{12}{x+3}+\frac{12}{x-3}=3\] |
| \[\Rightarrow \]\[\frac{12x-36-12x+36}{{{x}^{2}}-9}=3\] |
| \[\Rightarrow \] \[3{{x}^{2}}-27=24x\] |
| \[\Rightarrow \] \[{{x}^{2}}-8x-9=0\] |
| \[\Rightarrow \] \[(x-9)(x+1)=0\] |
| \[\Rightarrow \] \[x\ne 1\] |
| \[\therefore \] \[x=9\,\,km/h\] |
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