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# A and B Can Do a Piece of Work in 20 Days and B in 15 Days. They Work Together for 2 Days and Then a Goes Away. in How Many Days Will B Finish the Remaining Work? - Mathematics

Course
ConceptTime and Work

#### Question

A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?

#### Solution

$\text{ It is given that A can finish the work in 20 days and B can finish the same work in 15 days } .$
$\therefore \text{ Work done by A in 1 day } = \frac{1}{20}$
$\text{ Work done by B in 1 day } = \frac{1}{15}$
$\therefore \text{ Work done by } \left( A + B \right) \text { in 1 day } = \frac{1}{20} + \frac{1}{15}$
$= \frac{3 + 4}{60} = \frac{7}{60}$
$\therefore \text{ Work done by } \left( A + B \right) \text{ in 2 days } = \frac{14}{60} = \frac{7}{30}$
$\text{ Remaining work } = 1 - \frac{7}{30} = \frac{23}{30}$
$\text{ It is given that the remaining work is done by B } .$
$\because \text{ Complete work is done by B in 15 days } .$
$\therefore \frac{23}{30} \text{ of the work will be done by B in } \left( 15 \times \frac{23}{30} \right) \text{ days or } \frac{23}{2} \text{ days or } 11\frac{1}{2} \text{ days } .$
$\text{ Thus, the remaining work is done by B in 11 } \frac{1}{2} \text{ days .}$

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Solution A and B Can Do a Piece of Work in 20 Days and B in 15 Days. They Work Together for 2 Days and Then a Goes Away. in How Many Days Will B Finish the Remaining Work? Concept: Time and Work.
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