A man purchases an item at 4/5th of its selling price and sold it at 12% more than its selling price. His gain will be

Options

A. `40%`
B. `50%`
C. `20%`
D. `30%`

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the Cost Price (CP) and Selling Price (SP)
The man purchases the item at \( \frac{4}{5} \) of its selling price. Let's denote the selling price as \( SP \). Therefore, the cost price can be calculated as:
\[ CP = \frac{4}{5} \times SP \]

### Step 2: Calculate the Selling Price
Let’s assume the selling price \( SP = 5 \) (for simplicity). Then, we can find the cost price:
\[ CP = \frac{4}{5} \times 5 = 4 \]

### Step 3: Calculate the Selling Price with Profit
The man sells the item at 12% more than its selling price. To find the new selling price, we calculate:
\[ \text{Profit} = 12\% \text{ of } SP = \frac{12}{100} \times SP = 0.12 \times 5 = 0.6 \]
Thus, the new selling price (let's call it \( SP' \)) is:
\[ SP' = SP + \text{Profit} = 5 + 0.6 = 5.6 \]

### Step 4: Calculate the Gain
Now, we can find the gain by subtracting the cost price from the new selling price:
\[ \text{Gain} = SP' - CP = 5.6 - 4 = 1.6 \]

### Step 5: Calculate the Gain Percentage
To find the gain percentage, we use the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{CP} \right) \times 100 = \left( \frac{1.6}{4} \right) \times 100 = 40\% \]

### Final Answer
The gain percentage is \( 40\% \).

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