Question

A coffe jug was 4/5 filled with coffee.Some of it was poured into coffee cup.The jug was 7/10 filled with coffee in end.If 5ml coffee was poured from the jug into the cup then how much coffee was left in the jug

Answer 1

$$\begin{gathered} \mathrm{Suppose}\mathrm{that}\mathrm{the}\mathrm{capacity}\mathrm{of}\mathrm{the}\mathrm{coffee}\mathrm{jug}\mathrm{be}\mathrm{x}\mathrm{ml} \\ \mathrm{So}\mathrm{the}\mathrm{initil}\mathrm{amount}\mathrm{of}\mathrm{coffee}\mathrm{in}\mathrm{coffee}\mathrm{jug}\mathrm{is}, \\ \frac{4}{5}\mathrm{of}\mathrm{x}\mathrm{ml}=\frac{4}{5}\mathrm{ml} \\ \mathrm{The}\mathrm{amount}\mathrm{of}\mathrm{coffee}\mathrm{left}\mathrm{after}5\mathrm{ml}\mathrm{of}\mathrm{coffee}\mathrm{was}\mathrm{transfered}\mathrm{to}\mathrm{coffee}\mathrm{cup}. \\ \left(\frac{4}{5}\mathrm{x}-5\right)\mathrm{ml} \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{jug}\mathrm{was}\frac{7}{10}\mathrm{filled}\mathrm{with}\mathrm{coffee}\mathrm{in}\mathrm{the}\mathrm{end}. \\ \mathrm{This}\mathrm{implies}\mathrm{that}, \\ \frac{4}{5}\mathrm{x}-5=\frac{7}{10}\mathrm{x} \\ \frac{4}{5}\mathrm{x}-\frac{7}{10}\mathrm{x}=5 \\ \frac{8\mathrm{x}-7\mathrm{x}}{10}=5 \\ \frac{\mathrm{x}}{10}=5 \\ \mathrm{x}=50 \\ \mathrm{So}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{coffee}\mathrm{left}\mathrm{in}\mathrm{the}\mathrm{jug}\mathrm{is}, \\ \frac{7}{10}\mathrm{x}=\frac{7}{10}\times 50=7\times 5=\mathbf{35}\mathbf{}\mathbf{ml} \end{gathered}$$