he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.

Step 1.

When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.

Step 2.

When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.

Shortcut.

We are essentially replacing water in the mixture with pure milk.

Let W_o be the amount of water in the mixture originally = 8 litres.

Let W_r be the amount of water in the mixture after the replacements have taken place.

Then,{W_r}/{W_o}= (1-R/M)^n

where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.

Hence, {W_r}/{W_o} =(1/2)^2 =1/4

Therefore, "W_r ={W_o}/4= 8/4 = 2 litres

Reference: lofoya. com/Aptitude-Questions-And-Answers/Alligation-or-Mixture/l3p1 .htm

Hope it helps