A businessman buy 20 kg of wheat at Rs 15 per kg and 30 kg wheat at Rs 13 per kg. To earn the profit of `100/3`% on a kg at what rate per kg he should sell his mixture ?

Options

A. Rs 23.90
B. Rs 18.40
C. Rs 278
D. Rs 34

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total cost of wheat
The businessman buys:
- 20 kg of wheat at Rs. 15 per kg
- 30 kg of wheat at Rs. 13 per kg

**Total Cost Price (CP)**:
\[ \text{CP} = (20 \, \text{kg} \times 15 \, \text{Rs/kg}) + (30 \, \text{kg} \times 13 \, \text{Rs/kg}) \]
\[ \text{CP} = (300) + (390) = 690 \, \text{Rs} \]

### Step 2: Calculate the total quantity of wheat
**Total Quantity**:
\[ \text{Total Quantity} = 20 \, \text{kg} + 30 \, \text{kg} = 50 \, \text{kg} \]

### Step 3: Calculate the cost price per kg
**Cost Price per kg**:
\[ \text{Cost Price per kg} = \frac{\text{Total Cost Price}}{\text{Total Quantity}} = \frac{690 \, \text{Rs}}{50 \, \text{kg}} = 13.8 \, \text{Rs/kg} \]

### Step 4: Determine the desired profit percentage
The desired profit is \( \frac{100}{3}\% \). To convert this percentage into a fraction:
\[ \text{Profit Fraction} = \frac{100}{3} \div 100 = \frac{1}{3} \]

### Step 5: Calculate the selling price per kg
To find the selling price (SP) per kg, we need to add the profit to the cost price. The profit on the cost price of Rs. 13.8 per kg can be calculated as:
\[ \text{Profit} = \text{Cost Price per kg} \times \text{Profit Fraction} = 13.8 \times \frac{1}{3} = 4.6 \, \text{Rs} \]

Now, calculate the selling price:
\[ \text{Selling Price per kg} = \text{Cost Price per kg} + \text{Profit} = 13.8 + 4.6 = 18.4 \, \text{Rs/kg} \]

### Final Answer
The businessman should sell his mixture at Rs. 18.4 per kg.

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