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A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work? - Mathematics

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ConceptTime and Work

Question

A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?

Solution

\[\text{ It is given that A can finish the work in 40 days and B can finish the same work in 45 days }  . \]
\[ \therefore \text{ Work done by A in 1 day } = \frac{1}{40}\]
\[ \text{ Work done by B in 1 day } = \frac{1}{45}\]
\[ \therefore \text{ Work done by } \left( A + B \right) \text{ in 1 day }  = \frac{1}{40} + \frac{1}{45}\]
\[ = \frac{9 + 8}{360} = \frac{17}{360}\]
\[ \therefore \text{ Work done by } \left( A + B \right) \text{ in 10 days } = 10 \times \frac{17}{360} = \frac{17}{36}\]
\[ \text{ Remaining work  } = 1 - \frac{17}{36} = \frac{19}{36}\]
\[ \text{ It is given that the remaining work is done by B . }  \]
\[\text{ Complete work is done by B in 45 days }  . \]
\[ \therefore \frac{19}{36} \text{ of the work will be done by B in }  \left( 45 \times \frac{19}{36} \right) \text{ days or } 23\frac{3}{4} \text{ days .}  \]
\[\text{ Thus, the remaining work is done by B in 23} \frac{3}{4} \text{ days }  .\]

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Solution A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work? Concept: Time and Work.
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