| A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days will all of them together complete the work? [SSC (CISF) 2011] |
A) 16 days
B) 15 days
C) 12 days
D) 10 days
Correct Answer: A
Solution :
| Given, time taken by (A + B) = 18 days |
| (A + B)'s 1 day's work \[=\frac{1}{18}\] (i) |
| Similarly, (B + C)'s 1 day's work \[=\frac{1}{24}\] (ii) |
| (A + C)'s 1 day's work\[=\frac{1}{36}\] (iii) |
| On adding Eqs. (i), (ii) and (iii), we get |
| 2 (A + B + C)'s 1 day's work |
| \[=\frac{1}{18}+\frac{1}{24}+\frac{1}{36}=\frac{4+3+2}{72}=\frac{1}{8}\] |
| \[\therefore \](A + B + C)'s 1 day's work \[=\frac{1}{16}\] |
| \[\therefore \]A, B and C together will complete the work 16 days. |
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