Question

# Tick (✓) the correct answer: A and B together can do a piece of work in 12 days; B and C can do it in 20 days while C and A can do it in 15 days. A, B and C all working together can do it in (a) 6 days (b) 9 days (c) 10 days (d) $10\frac{1}{2}$ days

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Solution

## (c) 10 days $\left(\mathrm{A}+\mathrm{B}\right)\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{work}\mathrm{in}12\mathrm{days}.\phantom{\rule{0ex}{0ex}}\left(\mathrm{B}+\mathrm{C}\right)\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{work}\mathrm{in}20\mathrm{days}.\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}+\mathrm{A}\right) \mathrm{can}\mathrm{do}\mathrm{a}\mathrm{work}\mathrm{in}15\mathrm{days}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Now},\mathrm{we}\mathrm{have}:\phantom{\rule{0ex}{0ex}}\mathrm{Work}\mathrm{done}\mathrm{by}\left(\mathrm{A}+\mathrm{B}\right)\mathrm{in}1\mathrm{day}=\frac{1}{12}\phantom{\rule{0ex}{0ex}}\mathrm{Work}\mathrm{done}\mathrm{by}\left(\mathrm{B}+\mathrm{C}\right)\mathrm{in}1\mathrm{day}=\frac{1}{20}\phantom{\rule{0ex}{0ex}}\mathrm{Work}\mathrm{done}\mathrm{by}\left(\mathrm{C}+\mathrm{A}\right)\mathrm{in}1\mathrm{day}=\frac{1}{15}\phantom{\rule{0ex}{0ex}}\mathrm{Net}\mathrm{work}\mathrm{done}\mathrm{by}2\left(\mathrm{A}+\mathrm{B}+\mathrm{C}\right)=\frac{1}{12}+\frac{1}{20}+\frac{1}{15}=\frac{5+3+4}{60}=\frac{12}{60}=\frac{1}{5}\phantom{\rule{0ex}{0ex}}\mathrm{Net}\mathrm{work}\mathrm{done}\mathrm{by}\left(\mathrm{A}+\mathrm{B}+\mathrm{C}\right)\mathrm{in}1\mathrm{day}=\frac{1}{10}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{If}\mathrm{A},\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{work}\mathrm{together},\mathrm{they}\mathrm{will}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{in}10\mathrm{days}.$

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