The ratio of milk and water mixture of four containers are `5 : 3, 2 : 1, 3 : 2` and `4 : 5` respectively. In which container, is the quantity of milk relative to water minimum ?

Options

A. First
B. Second
C. Third
D. Fourth

Answer

To solve the problem of determining in which container the quantity of milk relative to water is minimum, we will analyze the ratios of milk to water in each container step by step.

### Step 1: Understand the Ratios
The ratios of milk to water in the four containers are given as follows:
1. Container 1: 5 : 3
2. Container 2: 2 : 1
3. Container 3: 3 : 2
4. Container 4: 4 : 5

### Step 2: Convert Ratios to Fractions
To compare the quantities of milk relative to water, we will convert each ratio into a fraction representing the proportion of milk to the total mixture.

1. **Container 1**:
\[ \text{Milk fraction} = \frac{5}{5 + 3} = \frac{5}{8} \]

2. **Container 2**:
\[ \text{Milk fraction} = \frac{2}{2 + 1} = \frac{2}{3} \]

3. **Container 3**:
\[ \text{Milk fraction} = \frac{3}{3 + 2} = \frac{3}{5} \]

4. **Container 4**:
\[ \text{Milk fraction} = \frac{4}{4 + 5} = \frac{4}{9} \]

### Step 3: Compare the Fractions
Now we will compare the fractions obtained for each container to find out which one has the minimum quantity of milk relative to water.

- Container 1: \(\frac{5}{8} = 0.625\)
- Container 2: \(\frac{2}{3} \approx 0.667\)
- Container 3: \(\frac{3}{5} = 0.6\)
- Container 4: \(\frac{4}{9} \approx 0.444\)

### Step 4: Identify the Minimum
From the calculated values, we can see:
- Container 1: 0.625
- Container 2: 0.667
- Container 3: 0.6
- Container 4: 0.444

The minimum fraction is in **Container 4**, which has a milk fraction of approximately 0.444.

### Conclusion
Thus, the container in which the quantity of milk relative to water is minimum is **Container 4**.

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