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# A and B Can Finish a Work in 20 Days. a Alone Can Do 1 5 Th of the Work in 12 Days. in How Many Days Can B Alone Do It? - Mathematics

Course
ConceptTime and Work

#### Question

A and B can finish a work in 20 days. A alone can do $\frac{1}{5}$  th of the work in 12 days. In how many days can B alone do it?

#### Solution

$\text{ It is given that A and B can finish the work in 20 days }.$
$\therefore \text{ Work done by } \left( A + B \right) \text{ in 1 day } = \frac{1}{20}$
$\text{ Now, A alone can do } \frac{1}{5}\text{ th of the work in 12 days } .$
$\therefore \text { Time taken by A alone to complete the work } = \left( 5 \times 12 \right) = 60 \text{ days}$
$\Rightarrow \text{ Work done by A in 1 day } = \frac{1}{60}$
$\text{ Now, work done by B in 1 day = Work done by } \left( A + B \right) \text{ in 1 day work - Work done by A in 1 day }$
$= \frac{1}{20} - \frac{1}{60}$
$= \frac{3 - 1}{60} = \frac{2}{60}$
$\text{ Thus, B alone can polish the floor in } \frac{60}{2}\text{ days or 30 days } .$

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#### APPEARS IN

Solution A and B Can Finish a Work in 20 Days. a Alone Can Do 1 5 Th of the Work in 12 Days. in How Many Days Can B Alone Do It? Concept: Time and Work.
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