A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.
(i) The rate of X is Rs. 20 per kg
(ii) The rate of Y is Rs. 13 per kg.

Answer

To find the profit percentage when a man mixes two types of rice (X and Y) and sells the mixture, we can follow these steps:

### Step 1: Understand the Problem
We need to find the profit percentage when the man sells a mixture of rice X and Y at Rs. 17 per kg. The cost of rice X is Rs. 20 per kg, and the cost of rice Y is Rs. 13 per kg.

### Step 2: Assume Quantities
Let's assume the man mixes 1 kg of rice X and 1 kg of rice Y. This means he has a total of 2 kg of rice mixture.

### Step 3: Calculate the Selling Price
The selling price of the mixture is given as Rs. 17 per kg. Therefore, for 2 kg, the total selling price (SP) will be:
\[ SP = 17 \text{ Rs/kg} \times 2 \text{ kg} = 34 \text{ Rs} \]

### Step 4: Calculate the Cost Price
Now, we need to calculate the cost price (CP) of the mixture:
- Cost of 1 kg of rice X = Rs. 20
- Cost of 1 kg of rice Y = Rs. 13

So, the total cost price for the mixture will be:
\[ CP = 20 \text{ Rs} + 13 \text{ Rs} = 33 \text{ Rs} \]

### Step 5: Calculate Profit
Now we can calculate the profit:
\[ \text{Profit} = SP - CP = 34 \text{ Rs} - 33 \text{ Rs} = 1 \text{ Rs} \]

### Step 6: Calculate Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{1 \text{ Rs}}{33 \text{ Rs}} \right) \times 100 \]
\[ \text{Profit Percentage} = \frac{100}{33} \approx 3.03\% \]

### Final Answer
The profit percentage is approximately **3.03%**.

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