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
$${A}'{s}\:\mathrm{Rate}\:\mathrm{of}\:\mathrm{work}\:=\:\frac{\mathrm{1}}{\mathrm{10}} \\ $$$${B}'{s}\:\mathrm{Rate}\:\mathrm{of}\:\mathrm{work}\:=\:\frac{\mathrm{1}}{\mathrm{5}} \\ $$$$\mathrm{Combined}\:\mathrm{Rate}\:\mathrm{of}\:\mathrm{work}\:=\:\frac{\mathrm{1}}{\mathrm{10}}\:+\:\frac{\mathrm{1}}{\mathrm{5}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{3}}{\mathrm{10}} \\ $$$$\therefore\:{A}\:\mathrm{and}\:{B}\:\mathrm{would}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\: \\ $$$$\:\:\:\:\mathrm{together}\:\mathrm{in}\:\frac{\mathrm{10}}{\mathrm{3}}\:\mathrm{days}. \\ $$$$\mathrm{But}\:{B}\:\mathrm{was}\:\mathrm{replaced}\:\mathrm{after}\:\mathrm{2}\:\mathrm{days}. \\ $$$$\mathrm{Now},\:\:\frac{\mathrm{2}}{\left(\mathrm{10}/\mathrm{3}\right)}\:×\mathrm{100}=\:\mathrm{60\%} \\ $$$$ \\ $$$$\mathrm{So}\:{A}\:\mathrm{and}\:{B}\:\mathrm{finished}\:\mathrm{60\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{job}\: \\ $$$$\mathrm{and}\:{A}\:\mathrm{and}\:{C}\:\mathrm{will}\:\mathrm{work}\:\mathrm{on}\:\mathrm{the}\:\mathrm{40\%}\:\mathrm{left} \\ $$$$\mathrm{which}\:\mathrm{they}\:\mathrm{finished}\:\mathrm{together}\:\mathrm{in}\:\mathrm{3}\:\mathrm{days}. \\ $$$$\Rightarrow\:\:\mathrm{it}\:\mathrm{will}\:\mathrm{take}\:{A}\:\mathrm{4}\:\mathrm{days}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{40\%}\: \\ $$$$\:\:\:\:\:\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{job},\:\mathrm{working}\:\mathrm{alone}. \\ $$$$ \\ $$$${Suppose}\:{C}\:{can}\:{finish}\:{the}\:{remaining} \\ $$$$\mathrm{40\%}\:{alone}\:{in}\:{x}\:{days},\:{then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{0}.\mathrm{4}}{{x}}\:\:+\:\:\frac{\mathrm{0}.\mathrm{4}}{\mathrm{4}}\:\:=\:\:\frac{\mathrm{0}.\mathrm{4}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:\:=\:\:\mathrm{12}\:\mathrm{days} \\ $$$$\:\mathrm{Hence},\:{C}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{40\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{work} \\ $$$$\:\mathrm{alone}\:\mathrm{in}\:\mathrm{12}\:\mathrm{days}. \\ $$$$\:\:\:\: \\ $$
Commented by bramlexs22 last updated on 18/Mar/21
$${waw}..={thanks} \\ $$
Answered by mr W last updated on 18/Mar/21
$${say}\:{A}\:{needs}\:{a}\:{days}\:{for}\:{the}\:{whole}\:{job}, \\ $$$${B}\:{needs}\:{b}\:{days},\:{C}\:{needs}\:{c}\:{days}. \\ $$$${given}:\:{a}=\mathrm{10},\:{b}=\mathrm{5} \\ $$$${in}\:{two}\:{days}\:{A}\:{and}\:{B}\:{did} \\ $$$$\mathrm{2}×\left(\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{5}}\right)=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${in}\:{three}\:{days}\:{A}\:{and}\:{C}\:{did}\:{the}\:{rest}: \\ $$$$\mathrm{3}×\left(\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{{c}}\right)=\mathrm{1}−\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\Rightarrow{c}=\mathrm{30} \\ $$$${C}\:{needs}\:\mathrm{30}\:{days}\:{to}\:{do}\:{the}\:{whole}\:{job}. \\ $$$${to}\:{do}\:\mathrm{40\%}\:{of}\:{the}\:{job},\:{C}\:{needs}\: \\ $$$$\mathrm{0}.\mathrm{4}×\mathrm{30}=\mathrm{12}\:{days} \\ $$
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
$${very}\:{simple} \\ $$