Venu mixed two varieties of wheat costing Rs 20 and Rs 25 per kg in the ratio 5:4 and sold the mixture at 24 per Kg Find the profit or loss in the whole transaction.

Options

A. 2% loss
B. 2%profit
C. 8% profit
D. 8% loss

Answer

To solve the problem step by step, we will first determine the cost price of the mixture and then calculate the selling price to find the profit or loss.

### Step 1: Determine the cost price of each variety of wheat.
- The cost of the first variety of wheat is Rs 20 per kg.
- The cost of the second variety of wheat is Rs 25 per kg.

### Step 2: Calculate the total cost for each variety based on the given ratio.
- The ratio of mixing is 5:4.
- Let the quantity of the first variety be 5 kg and the quantity of the second variety be 4 kg.

**Cost of the first variety:**
\[ \text{Cost of first variety} = 5 \, \text{kg} \times 20 \, \text{Rs/kg} = 100 \, \text{Rs} \]

**Cost of the second variety:**
\[ \text{Cost of second variety} = 4 \, \text{kg} \times 25 \, \text{Rs/kg} = 100 \, \text{Rs} \]

### Step 3: Calculate the total cost price of the mixture.
- Total cost price (CP) of the mixture:
\[ \text{Total CP} = 100 \, \text{Rs} + 100 \, \text{Rs} = 200 \, \text{Rs} \]

### Step 4: Calculate the total quantity of the mixture.
- Total quantity of the mixture:
\[ \text{Total quantity} = 5 \, \text{kg} + 4 \, \text{kg} = 9 \, \text{kg} \]

### Step 5: Determine the selling price of the mixture.
- Selling price (SP) is given as Rs 24 per kg.
- Total selling price of the mixture:
\[ \text{Total SP} = 9 \, \text{kg} \times 24 \, \text{Rs/kg} = 216 \, \text{Rs} \]

### Step 6: Calculate the profit or loss.
- Profit or loss is calculated as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]
\[ \text{Profit} = 216 \, \text{Rs} - 200 \, \text{Rs} = 16 \, \text{Rs} \]

### Step 7: Calculate the profit percentage.
- Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{16 \, \text{Rs}}{200 \, \text{Rs}} \right) \times 100 = 8\% \]

### Final Answer:
The profit in the whole transaction is Rs 16, and the profit percentage is 8%.

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