A milk man has $80$ litres of mixture which contains $40\%$ water. If he sells $20$ litres of the mixture to his customers and adds $x$ litres of pure milk to the remaining, then the ratio of milk to water in the mixture becomes $13:2$. Find the value of $x$ ( in litres ).

After selling 20 litres, the remaining 60 litres of mixture contains 60 percent milk and 40 percent water, which is 36 litres of milk and 24 litres of water. When x litres of pure milk are added, the ratio of milk to water becomes (36 plus x) divided by 24. This ratio is given as 13 divided by 2, so solving (36 plus x) divided by 24 equals 13 divided by 2 yields 72 plus 2x equals 312. Therefore, 2x equals 240 and x equals 120 litres.

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