Krishna has 12 oranges. He sells x of them at a profit of 10% and remaining at a loss of 10%. He gains 5% on the whole outlay. The value of x is.

Answer

To solve the problem step by step, we can break down the transactions involving the oranges sold by Krishna.

### Step 1: Understand the problem
Krishna has 12 oranges. He sells 'x' oranges at a profit of 10% and the remaining (12 - x) oranges at a loss of 10%. The overall gain on the entire transaction is 5%.

### Step 2: Define the cost price
Let's assume the cost price (CP) of each orange is ₹1. Therefore, the total cost price for 12 oranges is:
\[ \text{Total CP} = 12 \times 1 = ₹12 \]

### Step 3: Calculate selling prices
1. **Selling price for 'x' oranges sold at 10% profit:**
- Profit = 10% of CP
- Selling Price (SP) for each orange = CP + Profit = ₹1 + (10% of ₹1) = ₹1 + ₹0.10 = ₹1.10
- Total SP for 'x' oranges = \( x \times 1.10 = 1.10x \)

2. **Selling price for (12 - x) oranges sold at 10% loss:**
- Loss = 10% of CP
- Selling Price (SP) for each orange = CP - Loss = ₹1 - (10% of ₹1) = ₹1 - ₹0.10 = ₹0.90
- Total SP for (12 - x) oranges = \( (12 - x) \times 0.90 = 10.80 - 0.90x \)

### Step 4: Calculate total selling price
The total selling price (SP) for all 12 oranges is:
\[ \text{Total SP} = \text{SP from profit oranges} + \text{SP from loss oranges} \]
\[ \text{Total SP} = 1.10x + (10.80 - 0.90x) \]
\[ \text{Total SP} = 1.10x + 10.80 - 0.90x = 0.20x + 10.80 \]

### Step 5: Set up the equation for overall gain
According to the problem, Krishna gains 5% on the whole outlay:
- Total gain = 5% of Total CP
- Total gain = 5% of ₹12 = ₹0.60
- Therefore, Total SP = Total CP + Total gain = ₹12 + ₹0.60 = ₹12.60

Now we can set up the equation:
\[ 0.20x + 10.80 = 12.60 \]

### Step 6: Solve for 'x'
To find 'x', we can rearrange the equation:
\[ 0.20x = 12.60 - 10.80 \]
\[ 0.20x = 1.80 \]
\[ x = \frac{1.80}{0.20} \]
\[ x = 9 \]

### Conclusion
The value of 'x' is 9. This means Krishna sold 9 oranges at a profit of 10%.

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