In what ratio must sugar at Rs. 2 per kg be mixed with sugar at Rs. 5.50 per kg so that the mixture be worth RS-2.50 per kg?

Options

A. A)`2:1`
B. B)`1:5`
C. C)`6:1 `
D. D)`2:3`

Answer

To solve the problem of mixing two types of sugar at different prices to achieve a desired price for the mixture, we can use the method of alligation. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Prices
We have two types of sugar:
- Sugar A (Rs. 2 per kg)
- Sugar B (Rs. 5.50 per kg)

We want to mix these to achieve a mixture worth Rs. 2.50 per kg.

### Step 2: Set Up the Alligation
We will use the alligation method to find the ratio in which the two sugars should be mixed. The formula for alligation is:

\[ \text{Ratio} = \frac{\text{Price of Sugar B} - \text{Price of Mixture}}{\text{Price of Mixture} - \text{Price of Sugar A}} \]

### Step 3: Calculate the Differences
1. Calculate the difference between the price of Sugar B and the price of the mixture:
\[ 5.50 - 2.50 = 3.00 \]
2. Calculate the difference between the price of the mixture and the price of Sugar A:
\[ 2.50 - 2.00 = 0.50 \]

### Step 4: Set Up the Ratio
Now, we can set up the ratio using the differences calculated:
\[ \text{Ratio} = \frac{3.00}{0.50} = 6 \]

### Step 5: Write the Final Ratio
Since we have the ratio of Sugar B to Sugar A, we can express it as:
- Sugar A : Sugar B = 1 : 6

Thus, the ratio in which the two types of sugar must be mixed is:
\[ \text{Sugar A : Sugar B} = 1 : 6 \]

### Conclusion
The final answer is that Sugar at Rs. 2 per kg must be mixed with Sugar at Rs. 5.50 per kg in the ratio of 1:6.

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