Manish brought 25 kg of rice at Rs. 32 per kg and 15 kg of rice at Rs. 36 per kg. what profit did he get when he mixed the two varieties together and sold it at Rs. 40.20 per kg ?

Options

A. `25%`
B. `40%`
C. `30%`
D. `20%`

Explanation

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

### Step 1: Calculate the Cost Price of Each Variety of Rice
1. **Cost of 25 kg of rice at Rs. 32 per kg:**
\[ \text{Cost Price (CP1)} = 25 \, \text{kg} \times 32 \, \text{Rs/kg} = 800 \, \text{Rs} \]

2. **Cost of 15 kg of rice at Rs. 36 per kg:**
\[ \text{Cost Price (CP2)} = 15 \, \text{kg} \times 36 \, \text{Rs/kg} = 540 \, \text{Rs} \]

### Step 2: Calculate the Total Cost Price of the Mixture
3. **Total Cost Price (CP) of the mixture:**
\[ \text{Total CP} = CP1 + CP2 = 800 \, \text{Rs} + 540 \, \text{Rs} = 1340 \, \text{Rs} \]

### Step 3: Calculate the Total Weight of the Mixture
4. **Total weight of the mixture:**
\[ \text{Total Weight} = 25 \, \text{kg} + 15 \, \text{kg} = 40 \, \text{kg} \]

### Step 4: Calculate the Selling Price of the Mixture
5. **Selling Price (SP) of the mixture when sold at Rs. 40.20 per kg:**
\[ \text{Total SP} = 40 \, \text{kg} \times 40.20 \, \text{Rs/kg} = 1608 \, \text{Rs} \]

### Step 5: Calculate the Profit
6. **Profit:**
\[ \text{Profit} = \text{Total SP} - \text{Total CP} = 1608 \, \text{Rs} - 1340 \, \text{Rs} = 268 \, \text{Rs} \]

### Step 6: Calculate the Profit Percentage
7. **Profit Percentage:**
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 = \left( \frac{268}{1340} \right) \times 100 \approx 20\% \]

### Final Answer
Manish's profit percentage when he mixed the two varieties of rice and sold it at Rs. 40.20 per kg is **20%**.

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