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Question

# Mohan takes 9 hours to mow a large lawn. He and Sohan together can mow it in 4 hours. How long will Sohan take to mow the lawn if he works alone?

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Solution

## $\mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{Mohan}\mathrm{to}\mathrm{do}\mathrm{the}\mathrm{work}=9\mathrm{hours}\phantom{\rule{0ex}{0ex}}\mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{Mohan}\mathrm{and}\mathrm{Sohan}\mathrm{to}\mathrm{do}\mathrm{the}\mathrm{work}=4\mathrm{hours}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{Mohan}=\frac{1}{9}\phantom{\rule{0ex}{0ex}}\mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{Mohan}\mathrm{and}\mathrm{Sohan}=\frac{1}{4}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{Sohan}=\frac{1}{4}-\frac{1}{9}\phantom{\rule{0ex}{0ex}}=\frac{9-4}{36}=\frac{5}{36}\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{Sohan}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{work}\mathrm{in}\frac{36}{5}\mathrm{hours}\mathrm{i}.\mathrm{e}.7\frac{1}{5}\mathrm{hours}.$

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