**Problem Statement:**

In a mixture of 110 liters, the ratio of milk and water is 3:8. We need to find out how much milk should be added to make the ratio 1:2.


**Solution:**

To solve this problem, we will follow these steps:

1. Find the amount of milk and water in the initial mixture.
2. Determine the amount of milk and water required to make the desired ratio.
3. Calculate the difference in the amount of milk needed.
4. Add the required amount of milk to the initial mixture.
5. Verify if the new ratio is achieved.


**Step 1: Find the amount of milk and water in the initial mixture**

Given that the ratio of milk and water in the initial mixture is 3:8, we can calculate the amounts as follows:

Let the amount of milk in the mixture be 3x liters.
So, the amount of water in the mixture will be 8x liters.

According to the problem, the total mixture is 110 liters. Therefore, we have:

3x + 8x = 110

Simplifying the equation:

11x = 110

Dividing both sides by 11:

x = 10

The amount of milk in the initial mixture is 3x = 3 * 10 = 30 liters.
The amount of water in the initial mixture is 8x = 8 * 10 = 80 liters.


**Step 2: Determine the amount of milk and water required to make the desired ratio**

We need to make the ratio 1:2, which means the new mixture should have one part milk and two parts water.

Let the amount of milk to be added be y liters.
So, the amount of water to be added will be 2y liters.

**Step 3: Calculate the difference in the amount of milk needed**

To achieve the desired ratio, we need to add enough milk to make the amount of milk equal to the amount of water.

The amount of milk needed is 2y - 30 liters (as we already have 30 liters of milk in the initial mixture).


**Step 4: Add the required amount of milk to the initial mixture**

We need to add the amount of milk calculated in the previous step to the initial mixture.

New amount of milk = 30 + (2y - 30) = 2y liters


**Step 5: Verify if the new ratio is achieved**

According to the problem, the total mixture should be 110 liters.
Therefore, we have:

2y + (80 + 2y) = 110

Simplifying the equation:

4y + 80 = 110

Subtracting 80 from both sides:

4y = 30

Dividing both sides by 4:

y = 7.5

So, we need to add 7.5 liters of milk to the initial mixture to achieve the desired ratio of 1:2.

By adding 7.5 liters of milk to the initial mixture, the new amount of milk will be:

2y = 2 * 7.5 = 15 liters

The new amount of water will be:

2 * (2y) = 2 * (2 * 7.5) = 30 liters

Therefore, the new mixture will have a ratio of 15:30, which simplifies to