| A and B working separately can do a piece of work in 9 and 15 days, respectively. If they work for a day alternately, with A beginning, then the work will be completed in [SSC (10+2) 2014] |
A) 10 days
B) 11 days
C) 9 days
D) 12 days
Correct Answer: D
Solution :
| Work done by A and B in 2 days |
| \[=\frac{1}{9}+\frac{1}{15}=\frac{5+3}{45}=\frac{8}{45}\] |
| \[\because \] They both work alternately. |
| \[\therefore \] Work done by both in 9 days \[=\frac{9}{2}\times \frac{8}{45}=\frac{4}{5}\] |
| Now, remaining work \[=1-\frac{4}{5}=\frac{1}{5}\] |
| Next day, B will do the work. |
| \[\therefore \] Time taken by B to complete the work |
| \[=\frac{1}{5}\times 15=3\,days\] |
| \[\therefore \] Total time taken to complete the work |
| \[=(9+3)\,days=12\,days\] |
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