| A and B can do a work in 12 days. B and C in 15 days. C and A in 20 days. If A, B and C work together, they will complete the work in |
A) 5 days
B) \[7\frac{5}{6}\,\,days\]
C) 10 days
D) \[15\frac{2}{3}\,\,days\]
Correct Answer: C
Solution :
| \[(A+B)\]can complete the work in 12 days. |
| \[\therefore \] \[(A+B)'s\] 1 day's of work \[=\frac{1}{12}\] |
| Similarly, \[(B+C)'s\] 1 day's of work \[=\frac{1}{15}\] |
| and \[(C+A)'s\] 1 day's of work \[=\frac{1}{20}\] |
| \[\therefore \] \[2\,(A+B+C)'s\]1 day's of work, |
| \[=\frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{5+4+3}{60}=\frac{1}{5}\] |
| \[\therefore \] \[(A+B+C)'s\] can complete the work in 10 days. |
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