The marked price of an article is twice the cost price. For a gain of `20%`, what should be the discount percentage?

Options

A. 20
B. 40
C. 45
D. 60

Answer

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

### Step 1: Define the Cost Price (CP)
Let the Cost Price (CP) of the article be \( CP = 100 \) (we can assume any value for simplicity).

### Step 2: Calculate the Marked Price (MP)
According to the question, the Marked Price (MP) is twice the Cost Price. Therefore,
\[ MP = 2 \times CP = 2 \times 100 = 200 \]

### Step 3: Calculate the Selling Price (SP) for a 20% Gain
To find the Selling Price (SP) that gives a gain of 20%, we can use the formula:
\[ SP = CP + (20\% \text{ of } CP) = CP + 0.2 \times CP = 1.2 \times CP \]
Substituting the value of CP:
\[ SP = 1.2 \times 100 = 120 \]

### Step 4: Determine the Discount Amount
Now, we need to find the discount amount. The discount is the difference between the Marked Price and the Selling Price:
\[ \text{Discount} = MP - SP = 200 - 120 = 80 \]

### Step 5: Calculate the Discount Percentage
To find the discount percentage, we use the formula:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{MP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Discount Percentage} = \left( \frac{80}{200} \right) \times 100 \]
\[ \text{Discount Percentage} = 0.4 \times 100 = 40\% \]

### Conclusion
The required discount percentage is **40%**.

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