In what ratio must a mixture of 20% milk strength be mixed with that of 60% milk strength so as to get a new mixture of 25% milk strength?

Options

A. `7:1`
B. `4:1`
C. `5:2`
D. `9:2`

Answer

To solve the problem of mixing two milk strengths (20% and 60%) to achieve a new mixture of 25%, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the strengths of the mixtures
We have two mixtures:
- Mixture A: 20% milk strength
- Mixture B: 60% milk strength

### Step 2: Identify the desired strength of the new mixture
The desired strength of the new mixture is 25%.

### Step 3: Set up the alligation
We will use the alligation method to find the ratio in which these two mixtures should be combined. We will calculate the differences between the strengths of the mixtures and the desired strength.

- Difference between the strength of Mixture B (60%) and the desired strength (25%):
\[ 60\% - 25\% = 35\% \]

- Difference between the strength of Mixture A (20%) and the desired strength (25%):
\[ 25\% - 20\% = 5\% \]

### Step 4: Set up the ratio using the differences
According to the alligation rule, the ratio of the two mixtures can be determined by the differences calculated above. The ratio of the quantities of Mixture A to Mixture B is given by:
\[ \text{Ratio of A to B} = \frac{\text{Difference of B}}{\text{Difference of A}} = \frac{35}{5} \]

### Step 5: Simplify the ratio
Now we simplify the ratio:
\[ \frac{35}{5} = 7 \]
Thus, the ratio of Mixture A (20% milk) to Mixture B (60% milk) is:
\[ 7:1 \]

### Conclusion
The two mixtures should be mixed in the ratio of **7:1** to achieve a new mixture of 25% milk strength.

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