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Question Number 136063 by liberty last updated on 18/Mar/21

$$$$ A and B can do a job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 40% of the job?\n

Answered by nadovic last updated on 18/Mar/21

$$A^{\prime }s\mathrm{Rate}\mathrm{of}\mathrm{work}=\frac{1}{10}$$ $$B^{\prime }s\mathrm{Rate}\mathrm{of}\mathrm{work}=\frac{1}{5}$$ $$\mathrm{Combined}\mathrm{Rate}\mathrm{of}\mathrm{work}=\frac{1}{10}+\frac{1}{5}$$ $$=\frac{3}{10}$$ $$\therefore A\mathrm{and}B\mathrm{would}\mathrm{complete}\mathrm{the}\mathrm{work}$$ $$\mathrm{together}\mathrm{in}\frac{10}{3}\mathrm{days}.$$ $$\mathrm{But}B\mathrm{was}\mathrm{replaced}\mathrm{after}2\mathrm{days}.$$ $$\mathrm{Now},\frac{2}{\left(10/3\right)}\times 100=60\mathrm{\%}$$ $$$$ $$\mathrm{So}A\mathrm{and}B\mathrm{finished}60\mathrm{\%}\mathrm{of}\mathrm{the}\mathrm{job}$$ $$\mathrm{and}A\mathrm{and}C\mathrm{will}\mathrm{work}\mathrm{on}\mathrm{the}40\mathrm{\%}\mathrm{left}$$ $$\mathrm{which}\mathrm{they}\mathrm{finished}\mathrm{together}\mathrm{in}3\mathrm{days}.$$ $$\Rightarrow \mathrm{it}\mathrm{will}\mathrm{take}A4\mathrm{days}\mathrm{to}\mathrm{finish}40\mathrm{\%}$$ $$\mathrm{of}\mathrm{the}\mathrm{job},\mathrm{working}\mathrm{alone}.$$ $$$$ $$SupposeCcanfinishtheremaining$$ $$40\mathrm{\%}aloneinxdays,then$$ $$\frac{0.4}{x}+\frac{0.4}{4}=\frac{0.4}{3}$$ $$x=12\mathrm{days}$$ $$\mathrm{Hence},C\mathrm{can}\mathrm{finish}40\mathrm{\%}\mathrm{of}\mathrm{the}\mathrm{work}$$ $$\mathrm{alone}\mathrm{in}12\mathrm{days}.$$ $$$$

Commented bybramlexs22 last updated on 18/Mar/21

$$waw..=thanks$$

Answered by mr W last updated on 18/Mar/21

$$sayAneedsadaysforthewholejob,$$ $$Bneedsbdays,Cneedscdays.$$ $$given:a=10,b=5$$ $$intwodaysAandBdid$$ $$2\times (\frac{1}{10}+\frac{1}{5})=\frac{3}{5}$$ $$inthreedaysAandCdidtherest:$$ $$3\times (\frac{1}{10}+\frac{1}{c})=1-\frac{3}{5}$$ $$\Rightarrow c=30$$ $$Cneeds30daystodothewholejob.$$ $$todo40\mathrm{\%}ofthejob,Cneeds$$ $$0.4\times 30=12days$$

Commented byotchereabdullai@gmail.com last updated on 18/Mar/21

$$\mathrm{i}\mathrm{like}\mathrm{it}!$$

Commented bybramlexs22 last updated on 18/Mar/21

$$verysimple$$

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