A milkman had 20 litres of pure milk. He removed some milk and added an equal amount of water. He repeated the process again. Now, the milk was only 64% pure. Find the amount of milk that he removed initially.Choices:- 4 litres 6 litres 6.6 litres 5 litres

The problem can be solved using the concept of successive reduction.

1. The milkman starts with 20 litres of pure milk.

2. He removes some amount of milk (let's call this x litres) and adds the same amount of water.

3. He repeats the process, so the amount of milk is reduced by the same fraction twice.

4. After these two operations, the milk is only 64% pure, which means that 64% of the original 20 litres is still milk.

5. We can set up the equation (1 - x/20)^2 = 0.64 to represent this situation.

6. Solving this equation for x gives us x = 3 litres.

So, the milkman initially removed 3 litres of milk. However, this option is not available in the choices. There might be a mistake in the problem or the choices.

Let's solve this step by step:

1. Let's assume the milkman removed 'x' litres of milk initially. So, after removing 'x' litres of milk and adding 'x' litres of water, the quantity of milk left would be (20 - x) litres and the total quantity of the mixture would be 20 litres.

2. The milkman repeated the process. So, he removed 'x' litres of the mixture (which is 64% milk and 36% water) and added 'x' litres of water. The quantity of milk left after this would be (20 - x) * 0.64 litres and the total quantity of the mixture would still be 20 litres.

3. According to the problem, after the second operation, the milk is 64% pure. So, the quantity of milk left after the second operation is 64% of the total quantity of the mixture, which is 0.64 * 20 = 12.8 litres.

4. Therefore, we can set up the equation (20 - x) * 0.64 = 12.8 to find the value of 'x'.

5. Solving the equation, we get x = 4.5 litres.

However, this option is not available in the choices. It seems there might be a mistake in the problem or the choices provided.

The problem can be solved using the concept of successive reduction.

Step 1: The milkman starts with 100% pure milk, which is 20 litres.

Step 2: He removes some milk and adds the same amount of water. Let's assume the amount he removes and adds is x litres.

Step 3: After the first operation, the amount of pure milk left is (20 - x) litres and the total solution is still 20 litres. So, the percentage of pure milk is now (20 - x)/20 * 100%.

Step 4: He repeats the process. So, the amount of pure milk left after the second operation is (20 - x) - x = (20 - 2x) litres and the total solution is still 20 litres. So, the percentage of pure milk is now (20 - 2x)/20 * 100%.

Step 5: According to the problem, after the second operation, the milk is 64% pure. So, we can set up the equation (20 - 2x)/20 * 100% = 64%.

Step 6: Solving the equation, we get x = 3.6 litres.

However, this value is not in the given choices. It seems there might be a mistake in the problem or the choices. The closest answer to 3.6 litres in the choices is 4 litres.