Two glasses of equal volume contain milk upto one - third and one fourth of their capacity respectively . They are then filled up water and the contents are mixed in a bowl . What is the ratio of milk and water in the bowl ?

Options

A. `2:7`
B. `5:12`
C. `5:13`
D. `7:17`

Answer

To solve the problem step by step, let's denote the volume of each glass as \( V \).

### Step 1: Calculate the volume of milk in each glass.
- **Glass 1** contains milk up to one-third of its capacity:
\[ \text{Milk in Glass 1} = \frac{1}{3}V \]

- **Glass 2** contains milk up to one-fourth of its capacity:
\[ \text{Milk in Glass 2} = \frac{1}{4}V \]

### Step 2: Calculate the volume of water in each glass.
- For **Glass 1**, the remaining volume is filled with water:
\[ \text{Water in Glass 1} = V - \frac{1}{3}V = \frac{2}{3}V \]

- For **Glass 2**, the remaining volume is filled with water:
\[ \text{Water in Glass 2} = V - \frac{1}{4}V = \frac{3}{4}V \]

### Step 3: Calculate the total volume of milk in the bowl.
- The total milk from both glasses when mixed in the bowl:
\[ \text{Total Milk} = \frac{1}{3}V + \frac{1}{4}V \]
To add these fractions, we need a common denominator, which is 12:
\[ \text{Total Milk} = \frac{4}{12}V + \frac{3}{12}V = \frac{7}{12}V \]

### Step 4: Calculate the total volume of water in the bowl.
- The total water from both glasses when mixed in the bowl:
\[ \text{Total Water} = \frac{2}{3}V + \frac{3}{4}V \]
Again, we need a common denominator, which is 12:
\[ \text{Total Water} = \frac{8}{12}V + \frac{9}{12}V = \frac{17}{12}V \]

### Step 5: Find the ratio of milk to water in the bowl.
- The ratio of milk to water is:
\[ \text{Ratio of Milk to Water} = \frac{\text{Total Milk}}{\text{Total Water}} = \frac{\frac{7}{12}V}{\frac{17}{12}V} \]
The \( V \) and \( 12 \) cancel out:
\[ \text{Ratio} = \frac{7}{17} \]

### Final Answer:
The ratio of milk to water in the bowl is \( 7:17 \).

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