Question

A pot contains $82$ litres of pure milk. $\frac{1}{3}$ of the milk is replaced by the same amount of water. Again $\frac{1}{3}$ of the mixture is replaced by that amount of water. The ratio of milk and water in the new mixture is?

Answer 1

Initial quantity of milk = 82 litres

After the first replacement, composition of the mixture is as follows: $\frac{164}{3}$ litres of milk and $\frac{82}{3}$ litres of water

Again, one third mixture is replaced with water:

Quantity of milk removed = $\frac{2}{3}\times \frac{82}{3}=\frac{164}{9}$ litres.

Quantity of water removed = $\frac{1}{3}\times \frac{82}{3}=\frac{82}{9}$ litres.

Remaining quantity of,

Milk = $\frac{164}{3}-\frac{164}{9}=\frac{328}{9}$ litres

Water = $\frac{82}{3}-\frac{82}{9}+\frac{82}{3}=\frac{410}{9}$ litres

Ratio of milk:water = $\frac{328}{410}$ = $4:5$