In what ratio sugar costing Rs. 38 per kg and Rs. 30 per kg be mixed with each other so that on selling mixture at Rs. 35.2 per kg there will be a profit of 10%?

Options

A. `1:3`
B. `3:7`
C. `13:7`
D. `9:4`

Answer

To solve the problem, we need to find the ratio in which two types of sugar (costing Rs. 38 per kg and Rs. 30 per kg) should be mixed so that when sold at Rs. 35.2 per kg, there is a profit of 10%.

### Step 1: Calculate the Cost Price (CP) of the Mixture
To find the cost price of the mixture that allows for a 10% profit when sold at Rs. 35.2 per kg, we first need to determine the cost price using the selling price (SP).

Given:
- Selling Price (SP) = Rs. 35.2 per kg
- Profit = 10%

We can use the formula:
\[ \text{Cost Price (CP)} = \frac{\text{Selling Price (SP)}}{1 + \text{Profit Percentage}} \]

Substituting the values:
\[ CP = \frac{35.2}{1 + 0.10} = \frac{35.2}{1.10} = 32 \]

### Step 2: Set Up the Alligation Formula
Now we have the cost price of the mixture (Rs. 32). We will use the alligation method to find the ratio of the two types of sugar.

Let:
- Cost Price of Sugar A (Rs. 38 per kg)
- Cost Price of Sugar B (Rs. 30 per kg)
- Cost Price of Mixture (Rs. 32 per kg)

Using the alligation method:
\[ \text{Difference between A and Mixture} = 38 - 32 = 6 \]
\[ \text{Difference between B and Mixture} = 32 - 30 = 2 \]

### Step 3: Calculate the Ratio
The ratio of the quantities of Sugar A to Sugar B is given by the inverse of the differences calculated:
\[ \text{Ratio} = \frac{\text{Difference of B}}{\text{Difference of A}} = \frac{2}{6} = \frac{1}{3} \]

### Step 4: Conclusion
Thus, the ratio in which sugar costing Rs. 38 per kg and Rs. 30 per kg should be mixed is **1:3**.

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