A shopkeeper blends two varieties of tea costing 18 and 13 per 100 gm in the ratio 7:3. He sells the blended variety at the rate of 18.15 per 100 gm. His percentage gain in the transaction is

Options

A. 0.1
B. 0.12
C. 0.14
D. 0.08

Answer

To solve the problem step by step, we will calculate the cost price (CP) of the blended tea and then determine the selling price (SP) to find the percentage gain.

### Step 1: Calculate the Cost Price of the Blended Tea
The shopkeeper blends two varieties of tea in the ratio of 7:3. The costs of the two varieties are:
- Tea A: ₹18 per 100 gm
- Tea B: ₹13 per 100 gm

To find the cost price of the blended tea, we will calculate the total cost for each variety based on the blending ratio.

**Calculation:**
- Cost of Tea A (7 parts):
\[ \text{Cost of Tea A} = 7 \times 18 = 126 \text{ (for 700 gm)} \]

- Cost of Tea B (3 parts):
\[ \text{Cost of Tea B} = 3 \times 13 = 39 \text{ (for 300 gm)} \]

- Total Cost Price (CP) for 1000 gm (700 gm + 300 gm):
\[ \text{Total CP} = 126 + 39 = 165 \]

- Cost Price per 100 gm:
\[ \text{CP per 100 gm} = \frac{165}{10} = 16.5 \]

### Step 2: Identify the Selling Price
The selling price (SP) of the blended tea is given as:
\[ \text{SP} = 18.15 \text{ per 100 gm} \]

### Step 3: Calculate the Gain
To find the gain, we will subtract the cost price from the selling price.

**Calculation:**
\[ \text{Gain} = \text{SP} - \text{CP} = 18.15 - 16.5 = 1.65 \]

### Step 4: Calculate the Percentage Gain
The percentage gain can be calculated using the formula:
\[ \text{Percentage Gain} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]

**Calculation:**
\[ \text{Percentage Gain} = \left( \frac{1.65}{16.5} \right) \times 100 = 10\% \]

### Final Answer
The percentage gain in the transaction is **10%**.

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