| A streamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of stream is 2 km/h, then the distance between the two ports is [SSC (CGL) 2007] |
A) 50 km
B) 60 km
C) 70 km
D) 80 km
Correct Answer: D
Solution :
| Let the distance between two ports be \[x\,\,km.\] |
| Let the speed of streamer in still water \[=y\,\,km/h\] |
| \[\therefore \] \[\frac{x}{y+2}=4\] (i) |
| and \[\frac{x}{y-2}=5\] (ii) |
| From Eqs. (i) and (ii), we get |
| \[4\,(y+2)=5\,(y-2)\] |
| \[\Rightarrow \] \[4y+8=5y-10\] |
| \[\Rightarrow \] \[5y-4y=10+8\]\[\Rightarrow \]\[y=18\text{km/h}\] |
| From Eq. (i), we get |
| \[\frac{x}{18+2}=4\]\[\Rightarrow \]\[x=4\times 20=80\,\,km\] |
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