| A and B alone can complete a work in 9 and 18 days, respectively. They worked together, however 3 days before the completion of the work A left. In how many days was the work completed? |
A) 13
B) 8
C) 6
D) 5
Correct Answer: B
Solution :
| Let the work is completed by A and B together in x days. |
| \[\therefore \] \[\frac{x-3}{9}+\frac{x}{18}=1\]\[\Rightarrow \]\[\frac{2x-6+x}{18}=1\] |
| \[\Rightarrow \] \[3x=24\]\[\Rightarrow \]\[x=8\] |
| Alternate Method |
| Here, \[x=9,\]\[y=18\]and \[t=3\] |
| \[\therefore \]Total number of days taken by A and 8 |
| \[=\frac{y\,\,(x+t)}{x+y}=\frac{18\,\,(9+3)}{9+18}=\frac{18\times 12}{27}=8\,\,\text{days}\] |
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