| B and C together can complete a work in 8 days. A and B together can complete the same work in 12 days and A and C together can complete the same work in 16 days. In how many days can A, B and C together complete the same work? |
A) \[3\frac{9}{13}\]
B) \[7\frac{5}{13}\]
C) \[7\frac{5}{12}\]
D) \[3\frac{5}{12}\]
E) None of these
Correct Answer: B
Solution :
| (B + C)'s 1 day's work \[=\frac{1}{8}\] (i) |
| (A + B)'s1 day's work \[=\frac{1}{12}\] ... (ii) |
| (A + C)'s 1day's work \[=\frac{1}{16}\] ... (iii) |
| On adding Eqs. (i), (ii) and (lii), we get |
| 2 (A + B + C)'s 1 day's work |
| \[=\frac{1}{8}+\frac{1}{12}+\frac{1}{16}=\frac{6+4+3}{48}=\frac{13}{48}\] |
| \[\Rightarrow \](A + B + C)'s 1 day's work \[=\frac{13}{96}\] |
| \[\therefore \]A, B and C together can complete the work in |
| \[=\frac{96}{13}=7\frac{5}{13}\,\,\text{days}\] |
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