A shopkeeper bought an article at `4/5` of its marked price and sold it at 16% more than the marked price. His gain, percentage is:

Options

A. `42%`
B. `48%`
C. `40%`
D. `45%`

Answer

To find the gain percentage of the shopkeeper, we can follow these steps:

### Step 1: Define the Marked Price (MP)
Let the marked price (MP) of the article be \( x \).

### Step 2: Calculate the Cost Price (CP)
The shopkeeper bought the article at \( \frac{4}{5} \) of the marked price. Therefore, the cost price (CP) is:
\[ CP = \frac{4}{5} \times x = \frac{4x}{5} \]

### Step 3: Calculate the Selling Price (SP)
The shopkeeper sold the article at 16% more than the marked price. Therefore, the selling price (SP) is:
\[ SP = MP + 16\% \text{ of } MP = x + 0.16x = 1.16x \]

### Step 4: Calculate the Profit
Profit can be calculated as:
\[ \text{Profit} = SP - CP = 1.16x - \frac{4x}{5} \]
To simplify this, we need a common denominator:
\[ \frac{4x}{5} = \frac{4x \times 1.16}{5 \times 1.16} = \frac{4.64x}{5} \]
Now, substituting this back:
\[ \text{Profit} = 1.16x - \frac{4x}{5} = \frac{5.8x}{5} - \frac{4x}{5} = \frac{1.8x}{5} \]

### Step 5: Calculate the Gain Percentage
Gain percentage is given by the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{\frac{1.8x}{5}}{\frac{4x}{5}} \right) \times 100 \]
This simplifies to:
\[ = \left( \frac{1.8}{4} \right) \times 100 = 0.45 \times 100 = 45\% \]

### Final Answer
The gain percentage is **45%**.

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