| A can do a piece of work in 15 days. With the help of A, B can do it in \[6\frac{2}{3}\] days. B can do it alone in |
| [SSC (CGL) 2014] |
A) 13 days
B) 8 days
C) 10 days
D) 12 days
Correct Answer: D
Solution :
| Total work done by A in 15 days. |
| \[\therefore \]A's one day work \[=\frac{1}{15}\] |
| A and B can do working together in \[6\frac{2}{3}\]days \[=\frac{20}{3}\] days. |
| \[\therefore \]One day work of A and \[B=\frac{3}{20}.\] |
| Let work done B alone be x days. |
| \[\therefore \]One day work of \[B=1/x\] |
| \[\therefore \] \[\frac{1}{x}+\frac{1}{15}=\frac{3}{20}\]\[\Rightarrow \]\[\frac{1}{x}=\frac{3}{20}-\frac{1}{15}\] |
| \[\Rightarrow \] \[\frac{1}{x}=\frac{9-4}{60}\]\[\Rightarrow \]\[\frac{1}{x}=\frac{5}{60}\] |
| \[\Rightarrow \] \[\frac{1}{x}=\frac{1}{12}\] |
| \[\therefore \]One day work of \[B=1/12\] |
| Hence, B alone can do complete work in 12 days. |
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