Tick (✓) the correct answer:
A and B together can do a piece of work in 12 days; B and C can do it in 20 days while C and A can do it in 15 days. A, B and C all working together can do it in
(a) 6 days
(b) 9 days
(c) 10 days
(d) $10 \frac{1}{2}$ days
(c) 10 days
$(\mathrm{A}+\mathrm{B})$ can do a work in 12 days.
$(\mathrm{B}+\mathrm{C})$ can do a work in 20 days.
$(\mathrm{C}+\mathrm{A})$ can do a work in 15 days.
Now, we have :
Work done by $(\mathrm{A}+\mathrm{B})$ in 1 day $=\frac{1}{12}$
Work done by $(\mathrm{B}+\mathrm{C})$ in 1 day $=\frac{1}{20}$
Work done by $(\mathrm{C}+\mathrm{A})$ in 1 day $=\frac{1}{15}$
Net work done by $2(\mathrm{~A}+\mathrm{B}+\mathrm{C})=\frac{1}{12}+\frac{1}{20}+\frac{1}{15}=\frac{5+3+4}{60}=\frac{12}{60}=\frac{1}{5}$
Net work done by $(\mathrm{A}+\mathrm{B}+\mathrm{C})$ in 1 day $=\frac{1}{10}$
$\therefore$ If $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ work together, they will complete the work in 10 days.
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