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Question Number 127607 by bramlexs22 last updated on 31/Dec/20

Answered by liberty last updated on 31/Dec/20

 A ⇒24 days    B ⇒ 15 days   C⇒ 12 days   A and B started worked 3 days ⇒ 3×((1/(15))+(1/(12))) work   ⇒(1/5)+(1/4) = (9/(20)) works    remaining works = 1−(9/(20)) = ((11)/(20))   A complete the remaining works⇒n ×(1/(24))=((11)/(20))   ⇒ n = ((24^6 ×11)/(20^5 )) = ((66)/5) days = 13(1/5) days

$$\:\mathrm{A}\:\Rightarrow\mathrm{24}\:\mathrm{days}\: \\ $$$$\:\mathrm{B}\:\Rightarrow\:\mathrm{15}\:\mathrm{days} \\ $$$$\:\mathrm{C}\Rightarrow\:\mathrm{12}\:\mathrm{days} \\ $$$$\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{started}\:\mathrm{worked}\:\mathrm{3}\:\mathrm{days}\:\Rightarrow\:\mathrm{3}×\left(\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{12}}\right)\:\mathrm{work} \\ $$$$\:\Rightarrow\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{4}}\:=\:\frac{\mathrm{9}}{\mathrm{20}}\:\mathrm{works}\: \\ $$$$\:\mathrm{remaining}\:\mathrm{works}\:=\:\mathrm{1}−\frac{\mathrm{9}}{\mathrm{20}}\:=\:\frac{\mathrm{11}}{\mathrm{20}} \\ $$$$\:\mathrm{A}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{works}\Rightarrow\mathrm{n}\:×\frac{\mathrm{1}}{\mathrm{24}}=\frac{\mathrm{11}}{\mathrm{20}} \\ $$$$\:\Rightarrow\:\mathrm{n}\:=\:\frac{\cancel{\mathrm{24}}\:^{\mathrm{6}} ×\mathrm{11}}{\cancel{\mathrm{20}}\:^{\mathrm{5}} }\:=\:\frac{\mathrm{66}}{\mathrm{5}}\:\mathrm{days}\:=\:\mathrm{13}\frac{\mathrm{1}}{\mathrm{5}}\:\mathrm{days}\: \\ $$

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