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-ta

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?

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 by bramlexs22 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 by otchereabdullai@gmail.com last updated on 18/Mar/21

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

Commented by bramlexs22 last updated on 18/Mar/21

$$verysimple$$

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