The ratio of milk and water in a mixture of 80 litre is 3:2. If some quantity of mixture taken out and then 4 litre of milk and 4 litre of water is added to the mixture then the ratio of milk and water become 4:3. What quantity of mixture was taken out initially? 

Let the quantity of mixture taken out initially be x litres. Initial ratio of milk and water = 3 : 2 Total mixture = 80 litres So, quantity of milk = 80 × (3/5) = 48 litres And, quantity of water = 80 × (2/5) = 32 litres Now, x litres of mixture is taken out. Milk taken out = x × (3/5) = 3x/5 litres Water taken out = x × (2/5) = 2x/5 litres Remaining milk = 48 – 3x/5 Remaining water = 32 – 2x/5 Now, 4 litres of milk and 4 litres of water are added. So, final quantity of milk = 48 – 3x/5 + 4 = 52 – 3x/5 Final quantity of water = 32 – 2x/5 + 4 = 36 – 2x/5 According to the question, {52 - {3x}/{5}}/{36 - {2x}/{5}} = {4}/{3} Or, 3(52 - {3x}/{5}) = 4(36 - {2x}/{5}) Or, 156 - {9x}/{5} = 144 - {8x}/{5} Or, 156 - 144 ={9x/5} - {8x/5} Or, 12 ={x/5} So, x = 60 Therefore, the quantity of mixture taken out initially = 60 litres.