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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

Course
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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