A girl buys 2 pigeons for ₹ 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. ₹ 112
B. ₹ 85
C. ₹ 70
D. can't be determined

Answer

To solve the problem step by step, let's denote the following:

- The total cost price (CP) of 2 pigeons = ₹182
- The selling price (SP) of the first pigeon sold at a loss of 5%
- The selling price (SP) of the second pigeon sold at a profit of 8%

### Step 1: Calculate the Cost Price of Each Pigeon
The cost price of each pigeon can be calculated as follows:
\[ \text{Cost Price of 1 pigeon} = \frac{\text{Total Cost Price}}{2} = \frac{182}{2} = ₹91 \]

### Step 2: Calculate the Selling Price of the First Pigeon
The first pigeon is sold at a loss of 5%. We can calculate the selling price (SP) of the first pigeon using the formula for loss:
\[ \text{SP} = \text{CP} - \text{Loss} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Substituting the values:
\[ \text{SP of first pigeon} = 91 \times \left(1 - \frac{5}{100}\right) = 91 \times 0.95 = ₹86.45 \]

### Step 3: Set Up the Equation for the Second Pigeon
Let the selling price of the second pigeon (which is sold at a profit of 8%) be \( Y \). The profit can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]
Thus, we can express the selling price of the second pigeon as:
\[ Y = 91 \times \left(1 + \frac{8}{100}\right) = 91 \times 1.08 = ₹98.28 \]

### Step 4: Calculate the Total Selling Price
Since the girl neither gains nor loses on the whole, the total selling price of both pigeons must equal the total cost price:
\[ \text{Total SP} = \text{SP of first pigeon} + \text{SP of second pigeon} \]
Substituting the values:
\[ 86.45 + Y = 182 \]

### Step 5: Solve for Y
Now, we can solve for \( Y \):
\[ Y = 182 - 86.45 = ₹95.55 \]

### Conclusion
The price of the pigeon which has been sold at a profit is:
\[ \text{SP of second pigeon} = ₹95.55 \]