Question Number 135354 by liberty last updated on 12/Mar/21
$${Algebra} \\ $$A & B together can finish a work in 24 days, B & C in 30 days. If C is 20% more efficient than B, then how many days are required for A alone to finish the work?
Answered by EDWIN88 last updated on 12/Mar/21
$$\left(\mathrm{1}\right)\:\mathrm{A\&B}\:\Rightarrow\mathrm{Work}\:=\:\mathrm{24}\left(\mathrm{V}_{\mathrm{A}} +\mathrm{V}_{\mathrm{B}} \right) \\ $$$$\:\Rightarrow\frac{\mathrm{W}}{\mathrm{24}}\:=\:\mathrm{V}_{\mathrm{A}} +\mathrm{V}_{\mathrm{B}} \:…\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{B\&C}\Rightarrow\:\mathrm{Work}=\:\mathrm{30}\left(\mathrm{V}_{\mathrm{B}} +\mathrm{V}_{\mathrm{C}} \right)\:,\:\mathrm{where}\:\mathrm{V}_{\mathrm{C}} =\frac{\mathrm{6}}{\mathrm{5}}\mathrm{V}_{\mathrm{B}} \\ $$$$\Rightarrow\:\frac{\mathrm{Work}}{\mathrm{30}}\:=\:\frac{\mathrm{11}}{\mathrm{5}}\:\mathrm{V}_{\mathrm{B}} \Rightarrow\mathrm{V}_{\mathrm{B}} =\:\frac{\mathrm{W}}{\mathrm{66}}…\left(\mathrm{ii}\right) \\ $$$$\Rightarrow\mathrm{V}_{\mathrm{A}} \:=\:\frac{\mathrm{W}}{\mathrm{24}}−\frac{\mathrm{W}}{\mathrm{66}}\:=\:\frac{\mathrm{7W}}{\mathrm{264}}\:;\:\mathrm{so}\:\mathrm{many}\:\mathrm{days}\:\mathrm{for} \\ $$$$\mathrm{A}\:\mathrm{alone}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{is}\:=\:\frac{\mathrm{264}}{\mathrm{7}}\:\approx\:\mathrm{37}.\mathrm{714}\:\mathrm{days} \\ $$$$ \\ $$