65 men can reap a field in 24 days. if the job is to be done in 20 days , how many more men have to be hired /?
it is direct or inverse

Dear Student,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{men} \mathrm{needed} \mathrm{to} \mathrm{reap} \mathrm{the} \mathrm{field} \mathrm{in} 20 \mathrm{days} = \mathrm{x} \\ \mathrm{Now}, \mathrm{it} \mathrm{is} \mathrm{given} \mathrm{that} 65 \mathrm{men} \mathrm{can} \mathrm{reap} \mathrm{the} \mathrm{field} \mathrm{in} 24 \mathrm{days}. \\ \mathrm{Since}, \mathrm{number} \mathrm{of} \mathrm{men} \mathrm{varies} \mathrm{inversely} \mathrm{with} \mathrm{number} \mathrm{of} \mathrm{days}, \mathrm{so} \\ 20\mathrm{x} = 24 \times 65 \\ \Rightarrow \mathrm{x} = 78 \\ \mathrm{Hence}, \mathrm{to} \mathrm{complete} \mathrm{the} \mathrm{job} \mathrm{in} 20 \mathrm{days}, 13 \mathrm{more} \mathrm{men} \mathrm{should} \mathrm{be} \mathrm{hired}. \end{gathered}$$


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