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A contractor undertakes to construct a road in 20 days and engages 12 workers. After 16 days he finds only 2/3 part of the work has been done. How many more workers should be now engage in order to finish the job in time?

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Please find below the solution to the asked query :

$12\mathrm{Workers}\mathrm{complete}\frac{2}{3}\mathrm{Part}\mathrm{of}\mathrm{work}\mathrm{in}16\mathrm{days}.\phantom{\rule{0ex}{0ex}}\mathrm{Let}\mathrm{us}\mathrm{assume}\mathrm{x}\mathrm{men}\mathrm{required}\mathrm{to}\mathrm{complete}\mathrm{remaining}\frac{1}{3}\mathrm{part}\mathrm{of}\mathrm{work}\mathrm{in}4\mathrm{days}.\phantom{\rule{0ex}{0ex}}\mathrm{Now},\phantom{\rule{0ex}{0ex}}\frac{12\times 16}{{\displaystyle \frac{2}{3}}}=\frac{\mathrm{x}\times 4}{{\displaystyle \frac{1}{3}}}\phantom{\rule{0ex}{0ex}}\frac{12\times 16\times 3}{2}=\mathrm{x}\times 4\phantom{\rule{0ex}{0ex}}\frac{12\times 16\times 3}{2\times 4}=\mathrm{x}\phantom{\rule{0ex}{0ex}}\mathrm{x}=72\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{more}\mathrm{workers}\mathrm{required}=72-12\phantom{\rule{0ex}{0ex}}=60\mathrm{ANS}...$

$12\mathrm{Workers}\mathrm{complete}\frac{2}{3}\mathrm{Part}\mathrm{of}\mathrm{work}\mathrm{in}16\mathrm{days}.\phantom{\rule{0ex}{0ex}}\mathrm{Let}\mathrm{us}\mathrm{assume}\mathrm{x}\mathrm{men}\mathrm{required}\mathrm{to}\mathrm{complete}\mathrm{remaining}\frac{1}{3}\mathrm{part}\mathrm{of}\mathrm{work}\mathrm{in}4\mathrm{days}.\phantom{\rule{0ex}{0ex}}\mathrm{Now},\phantom{\rule{0ex}{0ex}}\frac{12\times 16}{{\displaystyle \frac{2}{3}}}=\frac{\mathrm{x}\times 4}{{\displaystyle \frac{1}{3}}}\phantom{\rule{0ex}{0ex}}\frac{12\times 16\times 3}{2}=\mathrm{x}\times 4\phantom{\rule{0ex}{0ex}}\frac{12\times 16\times 3}{2\times 4}=\mathrm{x}\phantom{\rule{0ex}{0ex}}\mathrm{x}=72\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{more}\mathrm{workers}\mathrm{required}=72-12\phantom{\rule{0ex}{0ex}}=60\mathrm{ANS}...$

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