A drum contains 20 litres of a paint. From this, 2 litres of paint is

1.	A drum contains 20 litres of a paint. From this, 2 litres of paint is taken out and replaced by 2 litres of oil. Again 2 litres of this mixture is taken out and replaced by 2 litres of oil. If this operation is performed once again, then what would be the final ratio of paint and oil in the drum ?
Answer» After the first operation, Paint = 18 litres, Oil = 2 litres After the second operation, Paint = 18 - \(\frac{18}{20}\times2\) = 16.2 litres, Oil = 2 – \(\frac{2}{20}\times2+2\) = 3.8 litres After the third operation, Paint = 16.2 - \(\frac{16.2}{20}\times2\) = 14.58 litres Oil = 3.8 - \(\frac{3.8}{20}\times2+2\) = 5.42 litres ∴ Required ratio = \(\frac{14.58}{5.42} = \frac{729}{271}\)

A drum contains 20 litres of a paint. From this, 2 litres of paint is taken out and replaced by 2 litres of oil. Again 2 litres of this mixture is taken out and replaced by 2 litres of oil. If this operation is performed once again, then what would be the final ratio of paint and oil in the drum ?

Answer»

After the first operation,

Paint = 18 litres, Oil = 2 litres

After the second operation,

Paint = 18 - \(\frac{18}{20}\times2\) = 16.2 litres,

Oil = 2 – \(\frac{2}{20}\times2+2\) = 3.8 litres

After the third operation,

Paint = 16.2 - \(\frac{16.2}{20}\times2\) = 14.58 litres

Oil = 3.8 - \(\frac{3.8}{20}\times2+2\) = 5.42 litres

∴ Required ratio = \(\frac{14.58}{5.42} = \frac{729}{271}\)