A and B 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? [NICL (AO) 2014] |
A) 16
B) 15
C) 12
D) 10
E) 17
Correct Answer: A
Solution :
\[(A+B)'s\] one day work \[=\frac{1}{18}\] .(i) |
\[(B+C)'s\]one day work \[=\frac{1}{24}\] .(ii) |
and \[(A+C)'s\] one day works \[=\frac{1}{36}\] .(iii) |
On adding Eqs. (i), (ii) and (iii), we get |
\[2\,(A+B+C)=\frac{1}{18}+\frac{1}{24}+\frac{1}{36}\] |
\[=\frac{4+3+2}{72}=\frac{9}{72}=\frac{1}{8}\] |
\[\Rightarrow \] \[(A+B+C)'s\] one day work \[=\frac{1}{2\times 8}=\frac{1}{16}\] |
So, A, B and C will together complete the work in |
16 days. |
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