Question

A tin of oil was 4/5 full.When 6 bottles of oil were taken out and 4 bottles of oil were poured into it,it was 3/4 full.How many bottles of oil can the tin contain?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{total}\mathrm{capacity}\mathrm{of}\mathrm{oil}\mathrm{tin}=\mathrm{x}\mathrm{litres} \\ \mathrm{Amount}\mathrm{of}\mathrm{oil}\mathrm{in}\mathrm{the}\mathrm{tin}=\frac{4\mathrm{x}}{5}\mathrm{litres} \\ \mathrm{Let}\mathrm{the}\mathrm{capacity}\mathrm{of}1\mathrm{bottle}=\mathrm{y}\mathrm{litres} \\ \mathrm{capacity}\mathrm{of}6\mathrm{bottles}=6\mathrm{y}\mathrm{litres} \\ \mathrm{capacity}\mathrm{of}4\mathrm{bottles}=4\mathrm{y}\mathrm{litres} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \frac{4\mathrm{x}}{5}-6\mathrm{y}+4\mathrm{y}=\frac{3\mathrm{x}}{4} \\ \Rightarrow \frac{4\mathrm{x}}{5}-2\mathrm{y}=\frac{3\mathrm{x}}{4} \\ \Rightarrow 2\mathrm{y}=\frac{4\mathrm{x}}{5}-\frac{3\mathrm{x}}{4} \\ \Rightarrow 2\mathrm{y}=\frac{16\mathrm{x}-15\mathrm{x}}{20} \\ \Rightarrow \mathrm{y}=\frac{\mathrm{x}}{40} \\ \mathrm{So},\mathrm{capacitiy}\mathrm{of}1\mathrm{bottle}=\frac{\mathrm{x}}{40}\mathrm{litres} \\ \mathrm{Number}\mathrm{of}\mathrm{bottles}\mathrm{of}\mathrm{oil}\mathrm{that}\mathrm{tin}\mathrm{can}\mathrm{contain}=\frac{\mathrm{capacity}\mathrm{of}\mathrm{tin}}{\mathrm{capacity}\mathrm{of}1\mathrm{bottle}}=\frac{\mathrm{x}}{\mathrm{x}/40}=40 \end{gathered}$$