| A and B together can do a work in 10 days. B and C together can do the same work in 6 days. A and C together can do the work in 12 days. Then, A, B and C together can do the work in [SSC (CGL) 2011] |
A) \[28\,\,\text{days}\]
B) \[14\,\,\text{days}\]
C) \[5\frac{5}{7}\text{days}\]
D) \[\text{8}\frac{2}{7}\text{days}\]
Correct Answer: C
Solution :
| Given, (A + B)'s 1 day's work \[=\frac{1}{10}\] (i) |
| (B + C)'s1 day's works \[=\frac{1}{6}\] ... (ii) |
| (C + A)'s 1 day's work\[=\frac{1}{12}\] (iii) |
| On adding Eqs. (i), (ii) and (iii), we get |
| 2 (A + B + C)'s 1 day's work \[=\frac{1}{10}+\frac{1}{6}+\frac{1}{12}\] |
| \[=\frac{6+10+5}{60}=\frac{21}{60}=\frac{7}{20}\] |
| \[\Rightarrow \](A + B + C)'s 1 day's work \[=\frac{7}{40}\] |
| \[\therefore \]All three together will complete the work in |
| \[=\frac{40}{7}=5\frac{5}{7}\,\,\text{days}\] |
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