A girl buy 2 pigeons for Rs. 182. She sells one at a loss of 5% and another at a profit if 8%. But she neither gains nor loses on the whole. Find the price of pigeon which has sold at a profit:

Options

A. Rs. 112
B. Rs. 85
C. Rs. 70
D. can't be determined

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Total Cost Price of the Pigeons
The girl buys 2 pigeons for Rs. 182. Therefore, the total cost price (CP) of both pigeons is:
\[ \text{Total CP} = 182 \text{ Rs} \]

### Step 2: Understand the Selling Conditions
She sells one pigeon at a loss of 5% and the other at a profit of 8%. The overall result is that she neither gains nor loses, which means her total selling price (SP) equals her total cost price (CP).

### Step 3: Set Up the Selling Price Equation
Let’s denote:
- The cost price of the pigeon sold at a loss (5%) as \( CP_1 \)
- The cost price of the pigeon sold at a profit (8%) as \( CP_2 \)

From the problem, we know:
\[ CP_1 + CP_2 = 182 \]

### Step 4: Calculate Selling Prices
The selling price of the first pigeon (sold at a loss of 5%):
\[ SP_1 = CP_1 - 0.05 \times CP_1 = 0.95 \times CP_1 \]

The selling price of the second pigeon (sold at a profit of 8%):
\[ SP_2 = CP_2 + 0.08 \times CP_2 = 1.08 \times CP_2 \]

### Step 5: Set Up the Total Selling Price Equation
Since she neither gains nor loses:
\[ SP_1 + SP_2 = CP_1 + CP_2 \]
Substituting the selling prices:
\[ 0.95 \times CP_1 + 1.08 \times CP_2 = 182 \]

### Step 6: Substitute CP_2 in Terms of CP_1
From the equation \( CP_1 + CP_2 = 182 \), we can express \( CP_2 \) as:
\[ CP_2 = 182 - CP_1 \]

Now substitute \( CP_2 \) into the selling price equation:
\[ 0.95 \times CP_1 + 1.08 \times (182 - CP_1) = 182 \]

### Step 7: Simplify the Equation
Expanding the equation:
\[ 0.95 \times CP_1 + 196.56 - 1.08 \times CP_1 = 182 \]
Combine like terms:
\[ (0.95 - 1.08) \times CP_1 + 196.56 = 182 \]
\[ -0.13 \times CP_1 + 196.56 = 182 \]

### Step 8: Solve for CP_1
Rearranging gives:
\[ -0.13 \times CP_1 = 182 - 196.56 \]
\[ -0.13 \times CP_1 = -14.56 \]
Dividing both sides by -0.13:
\[ CP_1 = \frac{14.56}{0.13} \]
\[ CP_1 = 112 \text{ Rs} \]

### Step 9: Find CP_2
Now substitute \( CP_1 \) back to find \( CP_2 \):
\[ CP_2 = 182 - CP_1 = 182 - 112 = 70 \text{ Rs} \]

### Conclusion
The price of the pigeon that was sold at a profit of 8% is:
\[ \text{Price of the pigeon sold at profit} = CP_2 = 70 \text{ Rs} \]