Two equal glasses are respectively 2/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a tumbler. The ratio of milk and water in the tumbler is

Options

A. `5 : 6`
B. ` 11 : 13`
C. ` 13 : 11`
D. Cannot be determined

Answer

To solve the problem step by step, we will first define the capacity of each glass and then calculate the amounts of milk and water in each glass before finding the ratio of milk to water in the tumbler.

### Step-by-Step Solution:

1. **Define the Capacity of Each Glass:**
Let the capacity of each glass be \( x \).

2. **Calculate the Amount of Milk in Each Glass:**
- In the first glass, the amount of milk is \( \frac{2}{3} \) of \( x \):
\[ \text{Milk in Glass 1} = \frac{2}{3}x \]
- In the second glass, the amount of milk is \( \frac{1}{4} \) of \( x \):
\[ \text{Milk in Glass 2} = \frac{1}{4}x \]

3. **Calculate the Amount of Water in Each Glass:**
- The amount of water in the first glass is the remaining volume after subtracting the milk:
\[ \text{Water in Glass 1} = x - \frac{2}{3}x = \frac{1}{3}x \]
- The amount of water in the second glass is:
\[ \text{Water in Glass 2} = x - \frac{1}{4}x = \frac{3}{4}x \]

4. **Total Amount of Milk:**
Now, we can calculate the total amount of milk in the tumbler:
\[ \text{Total Milk} = \text{Milk in Glass 1} + \text{Milk in Glass 2} = \frac{2}{3}x + \frac{1}{4}x \]
To add these fractions, we need a common denominator, which is 12:
\[ \text{Total Milk} = \frac{8}{12}x + \frac{3}{12}x = \frac{11}{12}x \]

5. **Total Amount of Water:**
Now, we calculate the total amount of water in the tumbler:
\[ \text{Total Water} = \text{Water in Glass 1} + \text{Water in Glass 2} = \frac{1}{3}x + \frac{3}{4}x \]
Again, we need a common denominator, which is 12:
\[ \text{Total Water} = \frac{4}{12}x + \frac{9}{12}x = \frac{13}{12}x \]

6. **Finding the Ratio of Milk to Water:**
Now we can find the ratio of milk to water:
\[ \text{Ratio of Milk to Water} = \frac{\text{Total Milk}}{\text{Total Water}} = \frac{\frac{11}{12}x}{\frac{13}{12}x} \]
The \( x \) and the \( 12 \) cancel out:
\[ \text{Ratio of Milk to Water} = \frac{11}{13} \]

### Final Answer:
The ratio of milk to water in the tumbler is \( 11:13 \).