Two similar pieces of an item were purchased by paying the same amount for each, and they were sold, respectively, for a profit of 25% and a loss of 20%. What was his profit percentage?

Options

A. 2
B. 4.5
C. 2.5
D. 5

Answer

To solve the problem, we need to calculate the overall profit percentage from the two transactions. Let's break it down step by step.

### Step 1: Define the cost price (CP)
Let the cost price of each piece be \( CP \).

### Step 2: Calculate the selling price (SP) for the first piece
The first piece is sold at a profit of 25%.
- Selling Price (SP1) = Cost Price + Profit
- Profit = 25% of CP = \( \frac{25}{100} \times CP = 0.25 \times CP \)
- Therefore,
\[ SP1 = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 3: Calculate the selling price (SP) for the second piece
The second piece is sold at a loss of 20%.
- Selling Price (SP2) = Cost Price - Loss
- Loss = 20% of CP = \( \frac{20}{100} \times CP = 0.20 \times CP \)
- Therefore,
\[ SP2 = CP - 0.20 \times CP = 0.80 \times CP \]

### Step 4: Calculate the total cost price and total selling price
- Total Cost Price (TCP) = Cost Price of first piece + Cost Price of second piece
\[ TCP = CP + CP = 2CP \]
- Total Selling Price (TSP) = Selling Price of first piece + Selling Price of second piece
\[ TSP = SP1 + SP2 = 1.25 \times CP + 0.80 \times CP = 2.05 \times CP \]

### Step 5: Calculate the overall profit
- Profit = Total Selling Price - Total Cost Price
\[ Profit = TSP - TCP = 2.05 \times CP - 2CP = 0.05 \times CP \]

### Step 6: Calculate the profit percentage
- Profit Percentage = \( \frac{Profit}{TCP} \times 100 \)
\[ Profit Percentage = \frac{0.05 \times CP}{2CP} \times 100 = \frac{0.05}{2} \times 100 = 2.5\% \]

### Final Answer
The overall profit percentage is **2.5%**.

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