Shiva purchased 280 kg of Rice at the rate of 15.60/kg and mixed it with 120 kg of rice purchased at the rate of 14.40/kg. He wants to earn a profit of Rs. 10.45 per kg by selling it. What should be the selling price of the mix per kg?

Options

A. a. Rs. 27.54
B. b. Rs. 26.94
C. c. Rs. 25.69
D. d. Rs. 22.18

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total cost of the first batch of rice.
Shiva purchased 280 kg of rice at the rate of Rs. 15.60 per kg.

\[ \text{Cost of first batch} = \text{Weight} \times \text{Rate} = 280 \, \text{kg} \times 15.60 \, \text{Rs/kg} = 4368 \, \text{Rs} \]

### Step 2: Calculate the total cost of the second batch of rice.
Shiva purchased 120 kg of rice at the rate of Rs. 14.40 per kg.

\[ \text{Cost of second batch} = \text{Weight} \times \text{Rate} = 120 \, \text{kg} \times 14.40 \, \text{Rs/kg} = 1728 \, \text{Rs} \]

### Step 3: Calculate the total cost of the mixed rice.
Now, we add the costs of both batches to find the total cost of the mixed rice.

\[ \text{Total Cost} = \text{Cost of first batch} + \text{Cost of second batch} = 4368 \, \text{Rs} + 1728 \, \text{Rs} = 6096 \, \text{Rs} \]

### Step 4: Calculate the total weight of the mixed rice.
The total weight of the mixed rice is the sum of the weights of both batches.

\[ \text{Total Weight} = 280 \, \text{kg} + 120 \, \text{kg} = 400 \, \text{kg} \]

### Step 5: Calculate the cost price per kg of the mixed rice.
To find the cost price per kg, we divide the total cost by the total weight.

\[ \text{Cost Price per kg} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{6096 \, \text{Rs}}{400 \, \text{kg}} = 15.24 \, \text{Rs/kg} \]

### Step 6: Calculate the desired selling price to achieve the profit.
Shiva wants to earn a profit of Rs. 10.45 per kg. Therefore, we add this profit to the cost price per kg to find the selling price.

\[ \text{Selling Price per kg} = \text{Cost Price per kg} + \text{Profit} = 15.24 \, \text{Rs/kg} + 10.45 \, \text{Rs/kg} = 25.69 \, \text{Rs/kg} \]

### Final Answer:
The selling price of the mix per kg should be Rs. 25.69.

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