A trader sells one type of sugar at 10 rupees per kg. and suffered a loss of 20%. While he sells the other type of sugar at Rs. 15 per kg and makes a profit of 25%. Now he mixes both type of sugar in equal proportion and sells the mixture at 18 rupees per kg. Find his profit and loss now-

Answer

To solve the problem step by step, we need to find the cost price (CP) of each type of sugar, the total cost price of the mixture, and then determine the profit or loss when the mixture is sold.

### Step 1: Calculate the Cost Price (CP) of the First Type of Sugar
- Selling Price (SP) of the first type of sugar = ₹10 per kg
- Loss = 20%

Using the formula for loss:
\[ \text{CP} = \frac{\text{SP} \times 100}{100 - \text{Loss \%}} \]
Substituting the values:
\[ \text{CP} = \frac{10 \times 100}{100 - 20} = \frac{1000}{80} = 12.5 \text{ rupees per kg} \]

### Step 2: Calculate the Cost Price (CP) of the Second Type of Sugar
- Selling Price (SP) of the second type of sugar = ₹15 per kg
- Profit = 25%

Using the formula for profit:
\[ \text{CP} = \frac{\text{SP} \times 100}{100 + \text{Profit \%}} \]
Substituting the values:
\[ \text{CP} = \frac{15 \times 100}{100 + 25} = \frac{1500}{125} = 12 \text{ rupees per kg} \]

### Step 3: Calculate the Total Cost Price of the Mixture
Since the trader mixes both types of sugar in equal proportions, we assume he takes 1 kg of each type:
- CP of 1 kg of first type = ₹12.5
- CP of 1 kg of second type = ₹12

Total CP of the mixture:
\[ \text{Total CP} = 12.5 + 12 = 24.5 \text{ rupees for 2 kg} \]

### Step 4: Calculate the Selling Price of the Mixture
Selling Price (SP) of the mixture = ₹18 per kg
For 2 kg:
\[ \text{Total SP} = 18 \times 2 = 36 \text{ rupees} \]

### Step 5: Calculate Profit or Loss
Profit or Loss = Total SP - Total CP
\[ \text{Profit} = 36 - 24.5 = 11.5 \text{ rupees} \]

### Step 6: Calculate Profit Percentage
Profit Percentage is calculated using the formula:
\[ \text{Profit \%} = \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit \%} = \left( \frac{11.5}{24.5} \right) \times 100 \]

Calculating:
\[ \text{Profit \%} = \left( \frac{11.5 \times 100}{24.5} \right) \approx 46.94\% \]

### Final Answer
The trader makes a profit of approximately **46.94%**.

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