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A, B and C Working Together Can Do a Piece of Work in 8 Hours. a Alone Can Do It in 20 Hours and B Alone Can Do It in 24 Hours. in How Many Hours Will C Alone Do the Same Work? - Mathematics

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ConceptTime and Work

Question

A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

Solution

\[\text{ Time taken by A to do the work = 20 hours } \]
\[\text{ Time taken by B to do the work = 24 hours} \]
\[\text{ Time taken by } \left( A + B + C \right) \text{ to do the work = 8 hours } \]
\[\text{ Now, } \]
\[ \text{ Work done by A } = \frac{1}{20}\]
\[ \text{ Work done by B } = \frac{1}{24}\]
\[ \text{ Work done by } \left( A + B + C \right) = \frac{1}{8}\]
\[ \therefore \text{ Work done by C } = \frac{1}{8} - \left( \frac{1}{20} + \frac{1}{24} \right)\]
\[ = \frac{1}{8} - \left( \frac{6}{120} + \frac{5}{120} \right) = \frac{1}{8} - \left( \frac{11}{120} \right)\]
\[ = \frac{15 - 11}{120} = \frac{4}{120} = \frac{1}{30}\]
\[\text{ Thus, C can do the work in 30 hours .} \]

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Solution A, B and C Working Together Can Do a Piece of Work in 8 Hours. a Alone Can Do It in 20 Hours and B Alone Can Do It in 24 Hours. in How Many Hours Will C Alone Do the Same Work? Concept: Time and Work.
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