Question

Gunpowder contains 75% nitre and 10% sulphur. Find the amount of the gunpowder which carries 9 kg nitre. What amount of gunpowder would contain 2.3 kg sulphur?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{gunpowder}\mathrm{that}\mathrm{contains}9\mathrm{kg}\mathrm{nitre}\mathrm{be}\mathrm{x}\mathrm{kg}. \\ \mathrm{i}.\mathrm{e}.,\frac{75}{100}\times \mathrm{x}=9 \\ \Rightarrow \frac{100}{75}=\frac{\mathrm{x}}{9} \\ \Rightarrow \mathrm{x}=\frac{900}{75} \\ \Rightarrow \mathrm{x}=12 \\ \therefore \mathrm{The}\mathrm{amount}\mathrm{of}\mathrm{gunpowder}\mathrm{containing}9\mathrm{kg}\mathrm{nitre}\mathrm{is}12\mathrm{kg}. \\ \mathrm{Let}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{gunpowder}\mathrm{containing}2.3\mathrm{kg}\mathrm{sulphur}\mathrm{be}\mathrm{y}\mathrm{kg}. \\ \mathrm{i}.\mathrm{e}.,\frac{10}{100}\times \mathrm{y}=2.3 \\ \Rightarrow \frac{100}{10}=\frac{\mathrm{y}}{2.3} \\ \Rightarrow \mathrm{y}=\frac{230}{10} \\ \Rightarrow \mathrm{y}=23 \\ \therefore \mathrm{The}\mathrm{amount}\mathrm{of}\mathrm{gunpowder}\mathrm{containing}2.3\mathrm{kg}\mathrm{sulphur}\mathrm{is}23\mathrm{kg}. \end{gathered}$$