# A And B Can Do A Piece Of Work In 12 Days, B And C In 15 Days While A And C Can Do It In 20 Days. At What Time C Alone Can Complete The Work?

Sol:

Given:

A and B can do a piece of work in 12 Days = $$\frac{1}{12}$$

B and C can do a piece of work in 15 Days = $$\frac{1}{15}$$

A and C can do a piece of work in 20 Days = $$\frac{1}{20}$$

Now by adding the above values, we get,

2(A + B + C) (One Day Work)

= $$\frac{1}{12} + \frac{1}{15} + \frac{1}{20}\frac{1}{12} + \frac{1}{15} + \frac{1}{20} \\ \Rightarrow \frac{5 + 4 + 3}{60}\\ \Rightarrow \frac{12}{60} \\ \Rightarrow \frac{1}{5}$$ work.

Therefore,

A + B + C (One Day Work) = $$\frac{1}{10}$$ work.

C (One Day Work) = [A + B + C (One Day Work)] – (A + B)(One Day Work)

$$\Rightarrow \frac{1}{10} – \frac{1}{12} \\ \Rightarrow \frac{6-5}{60} \\ \Rightarrow \frac{1}{60}$$

Therefore, C can complete the whole work in 60 days.

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