$$A$$ 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
Correct option is C. $$10$$ days
We know that,
Number of days required by $$A$$ and $$B$$ to complete the work $$=12$$ days
Number of days required by $$B$$ and $$C$$ to complete the work $$=20$$ days
Number of days required by $$C$$ and $$A$$ to complete the work $$=15$$ days
$$\therefore$$ We can calculate, work done by $$A$$ and $$B$$ in $$1$$ day $$=1/12$$
Work done by $$B$$ and $$C$$ in $$1$$ day $$=1/20$$
Work done by $$C$$ and $$A$$ in $$1$$ day $$=1/15$$
Now, work done by $$(A$$ and $$B)$$, $$(B$$ and $$C)$$, $$(C$$ and $$A)$$ together in $$1$$ day is given by
The sum is $$(A+B)+(B+C)+(C+A)=2(A+B+C)=1/12+1/20+1/15=12/60=1/5$$
Hence.
Work done by $$A, B, C=1/2\times 1/5=1/10$$
$$\therefore A, B, C$$ can do the work in $$10$$ days.