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?

Answer 1

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