A milkman has a mixture of milk and water in the ratio 7:4. He sells 55 litres of this mixture and adds 20 litres of pure water to the mixture. Now the ratio of milk and water becomes 7:6. Find the new quantity of the mixture.

The new quantity of the mixture is 130 litres.

Let milk = 7k and water = 4k, total = 11k.

After selling 55 litres, milk = 7k - 35 and water = 4k - 20.

Adding 20 litres water gives water = 4k, and (7k - 35)/4k = 7/6.

Solving, 42k - 210 = 28k, so k = 15 and total = 11 x 15 = 165.

Left after 55 sold and 20 added = 165 - 55 + 20 = 130 litres.