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?

Answer 1

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