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?



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.


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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