Question

A and B can polish the floors of a building in 10 days. A alone can do \[\frac{1}{4}\] th of it in 12 days. In how many days can B alone polish the floor  ?

 

 

Answer 1

\[\text{ It is given that A and B can polish the floors of the building in 10 days }  . \]
\[ \therefore \text{ Work done by }  \left( A + B \right) \text{ in 1 day }  = \frac{1}{10}\]
\[\text{ Now, A alone can do }  \frac{1}{4} \text{ th of the work in 12 days }  . \]
\[ \therefore \text{ Time taken by A alone to do the complete work } = \left( 4 \times 12 \right) = 48 \text{ days} \]
\[ \Rightarrow \text{ Work done by A in 1 day  }= \frac{1}{48}\]
\[ \text{ Now, work done by B in 1 day = Work done by } \left( A + B \right) \text{  in 1 day } - \text { Work done by A in 1 day } \]
\[ = \frac{1}{10} - \frac{1}{48}\]
\[ = \frac{24 - 5}{240} = \frac{19}{240}\]
\[ \text{ Thus, B alone can polish the floor in }  \frac{240}{19} \text{ days or } 12\frac{12}{19} \text{ days }  . \]