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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

Course
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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#### APPEARS IN

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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