| A cistern is normally filled in 8 h but takes another 2 h longer to till because of a leak in its bottom. If the cistern is full, then the leak will empty it in, [SSC (FCI) 2012] |
A) 16 h
B) 25 h
C) 20 h
D) 40 h
Correct Answer: D
Solution :
| Suppose, leak will empty the cistern in x h. |
| Pan filled of tank in \[1\,\,h=\frac{1}{8}-\frac{1}{x}=\frac{x-8}{8x}\] |
| \[\therefore \]Cistern will fill in \[\frac{8x}{8-x}h.\] |
| Again, \[\frac{8x}{-\,8+x}=8+2=10\] |
| \[\Rightarrow \] \[8x=-\,80+10x\] |
| \[\Rightarrow \] \[2x=80\]\[\Rightarrow \]\[x=40\] |
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