A vessel has 400 litres of pure milk. 40 litres of milk is removed from the vessel and replaced by water. 40 litres of the mixture thus formed is replaced by water. This procedure is repeated once again. Find the percentage of milk in the resultant solution.
Question
A vessel has 400 litres of pure milk. 40 litres of milk is removed from the vessel and replaced by water. 40 litres of the mixture thus formed is replaced by water. This procedure is repeated once again. Find the percentage of milk in the resultant solution.
Solution
Sure, let's solve this step by step:
Step 1: Initially, the vessel has 400 litres of pure milk.
Step 2: 40 litres of milk is removed and replaced by water. So, the quantity of milk in the vessel becomes 400 - 40 = 360 litres. The total quantity of the mixture in the vessel remains 400 litres.
Step 3: Now, 40 litres of the mixture is removed. The quantity of milk in these 40 litres will be (360/400)*40 = 36 litres. So, the quantity of milk left in the vessel after this step is 360 - 36 = 324 litres.
Step 4: Again, 40 litres of water is added to the vessel, keeping the total quantity of the mixture in the vessel 400 litres.
Step 5: Now, 40 litres of the mixture is removed again. The quantity of milk in these 40 litres will be (324/400)*40 = 32.4 litres. So, the quantity of milk left in the vessel after this step is 324 - 32.4 = 291.6 litres.
Step 6: Again, 40 litres of water is added to the vessel, keeping the total quantity of the mixture in the vessel 400 litres.
So, the percentage of milk in the resultant solution is (291.6/400)*100 = 72.9%.
Therefore, the resultant solution contains 72.9% milk.
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