Krishna purchased a number of articles at Rs.10 for each and the same number for Rs.14 each. He mixed them together and sold them for Rs.13 each. Then his gain or loss percent is

Options

A. Loss 8`1/3` %
B. Gain 8`2/3`%
C. Loss 8`2/3` %
D. Gain 8`1/3`%

Answer

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

### Step 1: Determine the number of articles purchased
Let’s assume Krishna purchased 10 articles at Rs. 10 each and 10 articles at Rs. 14 each.

### Step 2: Calculate the total cost price (CP)
- Cost of 10 articles at Rs. 10 each:
\[ \text{Cost for first type} = 10 \times 10 = 100 \text{ Rs.} \]
- Cost of 10 articles at Rs. 14 each:
\[ \text{Cost for second type} = 10 \times 14 = 140 \text{ Rs.} \]
- Total Cost Price (CP):
\[ \text{Total CP} = 100 + 140 = 240 \text{ Rs.} \]

### Step 3: Calculate the total selling price (SP)
- Total number of articles sold = 10 (from first type) + 10 (from second type) = 20 articles.
- Selling price for each article is Rs. 13.
- Total Selling Price (SP):
\[ \text{Total SP} = 20 \times 13 = 260 \text{ Rs.} \]

### Step 4: Calculate the gain or loss
- Gain = Total SP - Total CP:
\[ \text{Gain} = 260 - 240 = 20 \text{ Rs.} \]

### Step 5: Calculate the gain percentage
- Gain Percentage formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
- Plugging in the values:
\[ \text{Gain Percentage} = \left( \frac{20}{240} \right) \times 100 = \frac{20 \times 100}{240} = \frac{2000}{240} \]
- Simplifying:
\[ \text{Gain Percentage} = \frac{2000 \div 40}{240 \div 40} = \frac{50}{6} \approx 8.33\% \]

### Step 6: Final result
The gain percentage is approximately \( 8.33\% \).

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