We are given a mixture of water and milk in a 1:1 ratio, and we need to determine the percentage of milk in a new mixture after mixing 1/3 of this original mixture with an equal amount of pure milk.

Let’s break down the steps:

Step 1: Define the total quantity of the original mixture.

Let the total amount of the original mixture (water + milk) be $x$ liters. Since the ratio of water to milk is 1:1, the amount of water is $\frac{x}{2}$ liters and the amount of milk is $\frac{x}{2}$ liters.

Step 2: Take 1/3 of the original mixture.

The amount of mixture taken is $\frac{1}{3}$ of $x$, which is $\frac{x}{3}$ liters. Since the water and milk are in equal quantities in the original mixture:

• Amount of water in $\frac{x}{3}$ liters of mixture = $\frac{x}{6}$ liters
• Amount of milk in $\frac{x}{3}$ liters of mixture = $\frac{x}{6}$ liters

Step 3: Add an equal amount of pure milk.

We add $\frac{x}{3}$ liters of pure milk to the $\frac{x}{3}$ liters of mixture.

• New total amount of liquid = $\frac{x}{3} + \frac{x}{3} = \frac{2x}{3}$ liters
• New amount of milk = $\frac{x}{6}$ liters from the original mixture + $\frac{x}{3}$ liters of pure milk = $\frac{x}{6} + \frac{2x}{6} = \frac{3x}{6} = \frac{x}{2}$ liters
• New amount of water = $\frac{x}{6}$ liters (since no additional water is added)

Step 4: Calculate the percentage of milk in the new mixture.

The percentage of milk in the new mixture is: $\text{Percentage of milk} = \left( \frac{\text{Amount of milk}}{\text{Total amount of liquid}} \right) \times 100 = \left( \frac{\frac{x}{2}}{\frac{2x}{3}} \right) \times 100$ Simplifying: $\frac{\frac{x}{2}}{\frac{2x}{3}} = \frac{x}{2} \times \frac{3}{2x} = \frac{3}{4}$ Thus, the percentage of milk is: $\frac{3}{4} \times 100 = 75\%$

Final Answer:

The percentage of milk in the new mixture is 75%.

Would you like more details on any part of the explanation, or do you have any questions?

Here are 5 related questions:

1. What if the initial ratio of water to milk was 2:1?
2. How would the percentage change if 1/2 of the mixture was used instead of 1/3?
3. What if we mixed 1/4 of the original mixture with the same amount of pure milk?
4. How would the result change if the added liquid was pure water instead of pure milk?
5. What if we had an initial amount of 10 liters of the mixture? How much milk would be in the final mixture?

Tip: When dealing with ratios, always remember to break down the quantities of each component before making further calculations.