Question

Gunpowder contains 75% nitre and 10% sulphur. Find the amount of gunpowder which carries 9 kg nitre. What amount of gunpowder would contain 2.5 kg sulphur?

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{gunpowder}. \\ \mathrm{Amount}\mathrm{of}\mathrm{nitre}=75\% \\ \mathrm{Let}x\mathrm{kg}\mathrm{be}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{gunpowder}\mathrm{containing}9\mathrm{kg}\mathrm{of}\mathrm{nitre}. \\ \mathrm{i}.\mathrm{e}.,\left(75\%\mathrm{of}\mathrm{x}\right)=9\mathrm{kg} \end{gathered}$$
$$\begin{gathered} \Rightarrow \left(x\times \frac{75}{100}\right)=9 \\ \Rightarrow \frac{75x}{100}=9 \\ \Rightarrow x=\left(9\times \frac{100}{75}\right) \\ \Rightarrow x=12\mathrm{kg} \end{gathered}$$
$$\begin{gathered} \mathrm{Hence},12\mathrm{kg}\mathrm{of}\mathrm{gunpowder}\mathrm{contains}9\mathrm{kg}\mathrm{of}\mathrm{nitre}. \\ \mathrm{Now},\mathrm{amount}\mathrm{of}\mathrm{sulphur}=10\% \\ \mathrm{Let}x\mathrm{kg}\mathrm{be}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{gunpowder}\mathrm{containing}2.5\mathrm{kg}\mathrm{of}\mathrm{sulphur}. \\ \mathrm{i}.\mathrm{e}.,\left(10\%\mathrm{of}\mathrm{x}\right)=2.5\mathrm{kg} \end{gathered}$$
$$\begin{gathered} \Rightarrow \left(x\times \frac{10}{100}\right)=2.5 \\ \Rightarrow \frac{10x}{100}=2.5 \\ \Rightarrow \frac{x}{10}=2.5 \\ \Rightarrow x=\left(2.5\times 10\right) \\ \Rightarrow x=25\mathrm{kg} \end{gathered}$$
$\mathrm{Hence},25\mathrm{kg}\mathrm{of}\mathrm{gunpowder}\mathrm{contains}2.5\mathrm{kg}\mathrm{of}\mathrm{sulphur}.$