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Question

# Tick (✓) the correct answer: A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in (a) 24 days (b) 27 days (c) 36 days (d) 48 days

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Solution

## (c) 36 days $\mathrm{Let}\mathrm{A}\mathrm{take}x\mathit{}\mathrm{days}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{work}.\mathrm{Then}\mathrm{B}\mathrm{takes}2x\mathrm{days}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{work}.\phantom{\rule{0ex}{0ex}}\mathrm{A}\text{'}\mathrm{s}1\mathrm{day}\text{'}\mathrm{s}\mathrm{work}=\frac{1}{\mathrm{x}}\phantom{\rule{0ex}{0ex}}\mathrm{B}\text{'}\mathrm{s}1\mathrm{day}\text{'}\mathrm{s}\mathrm{work}=\frac{1}{2\mathrm{x}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{take}12\mathrm{days}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{work}.\phantom{\rule{0ex}{0ex}}\mathrm{Net}\mathrm{work}\mathrm{done}\mathrm{by}\left(\mathrm{A}+\mathrm{B}\right)\mathrm{in}1\mathrm{day}=\frac{1}{12}=\frac{1}{\mathrm{x}}+\frac{1}{2\mathrm{x}}=\frac{3}{2\mathrm{x}}\phantom{\rule{0ex}{0ex}}⇒2\mathrm{x}=36\phantom{\rule{0ex}{0ex}}⇒\mathrm{x}=18\phantom{\rule{0ex}{0ex}}\mathrm{A}\mathrm{can}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{by}\mathrm{himself}\mathrm{in}18\mathrm{days}.\phantom{\rule{0ex}{0ex}}\mathrm{B}\mathrm{will}\mathrm{take}36\mathrm{days},\mathrm{i}.\mathrm{e}.,\mathrm{twice}\mathrm{as}\mathrm{long}\mathrm{as}\mathrm{the}\mathrm{time}\mathrm{taken}\mathrm{by}\mathrm{A}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

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