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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

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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

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

  Is there an error in this question or solution?
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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