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# A and B Can Do a Piece of Work in 6 Days and 4 Days Respectively. a Started the Work; Worked at It for 2 Days and Then Was Joined by B. Find the Total Time Taken to Complete the Work. - Mathematics

Course
ConceptTime and Work

#### Question

A and B can do a piece of work in 6 days and 4 days respectively. A started the work; worked at it for 2 days and then was joined by B. Find the total time taken to complete the work.

#### Solution

$\text{ A can do a work in 6 days, and B can do the same work in 4 days } .$
$\therefore \text{ Work done by A in 2 days } = \frac{2}{6} = \frac{1}{3}$
$\text{ Remaining work } = 1 - \frac{1}{3} = \frac{2}{3}$
$\therefore \text{ Work done by } \left( A + B \right)\text{ in 1 day } = \left( \frac{1}{6} + \frac{1}{4} \right)$
$= \frac{2 + 3}{12} = \frac{5}{12}$
$\because \frac{5}{12}\text{ th work is done by A and B in 1 day } .$
$\therefore \frac{2}{3}\text{ rd work will be done by A and B in } \left( \frac{12}{5} \times \frac{2}{3} \right) \text{ days or } \frac{8}{5} \text{ days } .$
$\therefore \text{ Total time taken } = \left( \frac{8}{5} + 2 \right) \text{ days } = \frac{18}{5} \text{ days } = 3\frac{3}{5} \text{ days }$

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#### APPEARS IN

Solution A and B Can Do a Piece of Work in 6 Days and 4 Days Respectively. a Started the Work; Worked at It for 2 Days and Then Was Joined by B. Find the Total Time Taken to Complete the Work. Concept: Time and Work.
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