A, B and C together can complete a work in 12 days. A as well as B alone can do the same work in 36 days. In how many days can C alone complete the same work?

A, B, and C together complete the work in 12 days.

A alone can complete the work in 36 days.

B alone can complete the work in 36 days.

Work done per day =$$\frac{1}{\text{ Total number of days to complete the work}}$$ 

Work rate of A+B+C = $$\frac{1}{12}$$ 

Work rate of A alone = $$\frac{1}{36}$$ 

Work rate of B alone = $$\frac{1}{36}$$ 

Work rate of C alone = $$\frac{1}{x}$$​​

Now,  

​$$\frac{1}{36}+\frac{1}{36}+\frac{1}{x} = \frac{1}{12}$$  

​$$\frac{1}{x} = \frac{1}{12}-\frac{1}{36}-\frac{1}{36} \\ \ \\ \frac{1}{x} = \frac{1}{36}$$ 

So x = 36 days

therefore, C completes the work in 36 days.

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