| A man can row \[7\frac{1}{2}km/h\]in still water. If in a river running at \[1.5\,\,km/h,\] it takes him 50 min to row to a place and back, how far off is the place? |
A) \[3\,\,km\]
B) \[4\,\,km\]
C) \[1\,\,km\]
D) \[2\,\,km\]
Correct Answer: A
Solution :
| Let the distance be \[x\,\,km.\] |
| \[\because \]Speed of the man in still water \[=7\frac{1}{2}=7.5\,\,km/h\] |
| and speed of the river \[=1.5\,\,km/h\] |
| \[\therefore \]Speed of the man downstream \[=7.5+1.5=9\] |
| Speed the man upstream \[=7.5-1.5=6\,\,km/h\] |
| According to the question, \[\frac{x}{9}+\frac{x}{6}=\frac{50}{60}\] |
| \[\Rightarrow \]\[\frac{4x+6x}{36}=\frac{50}{60}\]\[\Rightarrow \]\[\frac{10x}{36}=\frac{50}{60}\]\[\Rightarrow \]\[\frac{50\times 36}{10\times 60}\] |
| \[\Rightarrow \]\[x=3\,\,km\] |
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