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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-




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?
$${Algebra} \\ $$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
(1) A&B ⇒Work = 24(V_A +V_B )   ⇒(W/(24)) = V_A +V_B  ...(i)  (2) B&C⇒ Work= 30(V_B +V_C ) , where V_C =(6/5)V_B   ⇒ ((Work)/(30)) = ((11)/5) V_B ⇒V_B = (W/(66))...(ii)  ⇒V_A  = (W/(24))−(W/(66)) = ((7W)/(264)) ; so many days for  A alone to finish is = ((264)/7) ≈ 37.714 days
$$\left(\mathrm{1}\right)\:\mathrm{A\&B}\:\Rightarrow\mathrm{Work}\:=\:\mathrm{24}\left(\mathrm{V}_{\mathrm{A}} +\mathrm{V}_{\mathrm{B}} \right) \\ $$$$\:\Rightarrow\frac{\mathrm{W}}{\mathrm{24}}\:=\:\mathrm{V}_{\mathrm{A}} +\mathrm{V}_{\mathrm{B}} \:…\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{B\&C}\Rightarrow\:\mathrm{Work}=\:\mathrm{30}\left(\mathrm{V}_{\mathrm{B}} +\mathrm{V}_{\mathrm{C}} \right)\:,\:\mathrm{where}\:\mathrm{V}_{\mathrm{C}} =\frac{\mathrm{6}}{\mathrm{5}}\mathrm{V}_{\mathrm{B}} \\ $$$$\Rightarrow\:\frac{\mathrm{Work}}{\mathrm{30}}\:=\:\frac{\mathrm{11}}{\mathrm{5}}\:\mathrm{V}_{\mathrm{B}} \Rightarrow\mathrm{V}_{\mathrm{B}} =\:\frac{\mathrm{W}}{\mathrm{66}}…\left(\mathrm{ii}\right) \\ $$$$\Rightarrow\mathrm{V}_{\mathrm{A}} \:=\:\frac{\mathrm{W}}{\mathrm{24}}−\frac{\mathrm{W}}{\mathrm{66}}\:=\:\frac{\mathrm{7W}}{\mathrm{264}}\:;\:\mathrm{so}\:\mathrm{many}\:\mathrm{days}\:\mathrm{for} \\ $$$$\mathrm{A}\:\mathrm{alone}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{is}\:=\:\frac{\mathrm{264}}{\mathrm{7}}\:\approx\:\mathrm{37}.\mathrm{714}\:\mathrm{days} \\ $$$$ \\ $$

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