Question

A vendor bought 10 dozen eggs at the rate of 22 rupees per dozen. Six of the eggs were rotten. He sold the remaining eggs at the rate of 2.50 rupees. What is his profit or loss percentage?

Answer 1

To determine the vendor's profit or loss percentage, let's follow these steps:

1. **Calculate the Total Cost Price (CP)**:
The vendor bought 10 dozen eggs at the rate of 22 rupees per dozen.

\[
\text{Total Cost Price} = \text{Number of dozens} \times \text{Cost per dozen}
\]
\[
\text{Total Cost Price} = 10 \times 22 = 220 \text{ rupees}
\]

2. **Calculate the Total Number of Eggs**:
One dozen equals 12 eggs. Therefore, the total number of eggs is:

\[
\text{Total Number of Eggs} = 10 \times 12 = 120 \text{ eggs}
\]

3. **Calculate the Number of Good Eggs**:
Since 6 eggs were rotten, the number of good eggs left is:

\[
\text{Number of Good Eggs} = 120 - 6 = 114 \text{ eggs}
\]

4. **Calculate the Total Selling Price (SP)**:
The vendor sells the good eggs at the rate of 2.50 rupees per egg.

\[
\text{Total Selling Price} = \text{Number of Good Eggs} \times \text{Selling Price per Egg}
\]
\[
\text{Total Selling Price} = 114 \times 2.50 = 285 \text{ rupees}
\]

5. **Calculate Profit or Loss**:
Now, we calculate the profit by subtracting the cost price from the selling price:

\[
\text{Profit} = \text{Total Selling Price} - \text{Total Cost Price}
\]
\[
\text{Profit} = 285 - 220 = 65 \text{ rupees}
\]

6. **Calculate Profit Percentage**:
The profit percentage can be calculated using the formula:

\[
\text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100
\]
\[
\text{Profit Percentage} = \left(\frac{65}{220}\right) \times 100 \approx 29.55\%
\]

Thus, the vendor made a profit of approximately **29.55%**.