The cost price of an article is 64% of the marked price. The gain percentage after allowing a discount of 12% on the marked price is

Options

A. `37.5%`
B. `48%`
C. `50.5%`
D. `52%`

Answer

To solve the problem step by step, we can follow these calculations:

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

### Step 2: Calculate the Cost Price (CP)
According to the problem, the cost price (CP) is 64% of the marked price (MP). Therefore, we can express the cost price as:
\[ CP = 0.64 \times x \]

### Step 3: Calculate the Selling Price (SP)
The problem states that a discount of 12% is allowed on the marked price. Thus, the selling price (SP) after the discount can be calculated as:
\[ SP = MP - \text{Discount} \]
The discount amount is:
\[ \text{Discount} = 12\% \text{ of } x = 0.12 \times x \]
So, the selling price becomes:
\[ SP = x - 0.12x = 0.88x \]

### Step 4: Calculate the Profit
Now, we can calculate the profit made on the sale:
\[ \text{Profit} = SP - CP \]
Substituting the values we found:
\[ \text{Profit} = 0.88x - 0.64x = 0.24x \]

### Step 5: Calculate the Profit Percentage
To find the gain percentage, we use the formula for profit percentage:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{0.24x}{0.64x} \right) \times 100 \]
The \( x \) cancels out:
\[ \text{Profit Percentage} = \left( \frac{0.24}{0.64} \right) \times 100 \]
Calculating the fraction:
\[ \frac{0.24}{0.64} = 0.375 \]
Now, multiplying by 100:
\[ \text{Profit Percentage} = 0.375 \times 100 = 37.5\% \]

### Final Answer
The gain percentage after allowing a discount of 12% on the marked price is **37.5%**.

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