Question

In an Army camp there are 800 soldiers. There is enough food for 60 days. If 400 more soldiers arrive at the camp, how many days will the food last?

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{are}\mathrm{given}\mathrm{that},\mathrm{in}\mathrm{an}\mathrm{army}\mathrm{camp},\mathrm{there}\mathrm{is}\mathrm{enough}\mathrm{food}\mathrm{for}800\mathrm{soldiers}\mathrm{for}60\mathrm{days}. \\ \mathrm{When}400\mathrm{more}\mathrm{soldiers}\mathrm{joined}\mathrm{the}\mathrm{camp},\mathrm{then}\mathrm{number}\mathrm{of}\mathrm{soldiers}\mathrm{become}1200. \\ \mathrm{Let}x\mathrm{be}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{days}\mathrm{for}\mathrm{which}\mathrm{the}\mathrm{food}\mathrm{last}\mathrm{when}\mathrm{there}\mathrm{are}1200\mathrm{soldiers}\mathrm{in}\mathrm{the}\mathrm{camp}. \end{gathered}$$

In tabular form,

Number of soldiers	800	1200
Number of days	60	x

$$\begin{gathered} \mathrm{Since}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{soldiers}\mathrm{and}\mathrm{number}\mathrm{of}\mathrm{days}\mathrm{for}\mathrm{which}\mathrm{the}\mathrm{food}\mathrm{last}\mathrm{varies}\mathrm{inversely},\mathrm{then} \\ 800\times 60=1200\times x \\ \Rightarrow x=\frac{48000}{1200} \\ \Rightarrow x=40 \\ \mathrm{So},\mathrm{number}\mathrm{of}\mathrm{days}\mathrm{for}\mathrm{which}\mathrm{the}\mathrm{food}\mathrm{last},\mathrm{when}\mathrm{there}\mathrm{are}1200\mathrm{soldiers}\mathrm{in}\mathrm{camp}\mathrm{is}40. \end{gathered}$$