| A can do a work in 12 days. When he had worked for 3 days, B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work? [SSC (CGL) 2011] |
A) 6 days
B) 12 days
C) 4 days
D) 8 days
Correct Answer: A
Solution :
| One day's work of \[A=\frac{1}{12}\] |
| \[\Rightarrow \] 3 day's work of \[A=\frac{3}{12}=\frac{1}{4}\] |
| \[\therefore \] Remaining work \[=1-\frac{1}{4}=\frac{3}{4}\] |
| Let B can do a work in x days. |
| Then, according to the question, |
| \[3\left( \frac{1}{12}+\frac{1}{x} \right)=\frac{3}{4}\] |
| \[\Rightarrow \] \[\frac{1}{4}+\frac{3}{x}=\frac{3}{4}\] |
| \[\Rightarrow \] \[\frac{3}{x}=\frac{2}{4}\]\[\Rightarrow \]\[x=\frac{12}{2}=6\,days\] |
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