After giving a dicount of 20% on an article, shopkeeper gains 20%. What is the percentage mark up ?

Options

A. 75
B. 66.67
C. 50
D. 33.33

Answer

To solve the problem step by step, let's define the terms and calculate the required percentage markup.

### Step 1: Define the Cost Price (CP) and Selling Price (SP)
Let's assume the Cost Price (CP) of the article is Rs. 100.

### Step 2: Calculate the Selling Price (SP) after Discount
Given that the shopkeeper gives a discount of 20% on the Marked Price (MP), we need to find out the Selling Price (SP) after this discount.

If the Marked Price (MP) is assumed to be Rs. 100, then:
- Discount = 20% of MP = 20% of Rs. 100 = Rs. 20
- Therefore, Selling Price (SP) = MP - Discount = Rs. 100 - Rs. 20 = Rs. 80

### Step 3: Determine the Profit
According to the problem, the shopkeeper gains a profit of 20%. This means:
- Profit = 20% of CP = 20% of Rs. 100 = Rs. 20
- Therefore, Selling Price (SP) can also be calculated as:
SP = CP + Profit = Rs. 100 + Rs. 20 = Rs. 120

### Step 4: Set the Selling Price Equal
From the previous steps, we have two expressions for Selling Price:
1. SP = Rs. 80 (after discount)
2. SP = Rs. 120 (based on profit)

Since the Selling Price must be the same, we can set these equal to each other:
- Rs. 80 = Rs. 120

### Step 5: Calculate the Marked Price (MP)
Since we assumed the Marked Price (MP) to be Rs. 100, we need to find the actual Marked Price that results in a Selling Price of Rs. 120 after a 20% discount.

Let MP be the actual Marked Price.
- After a 20% discount, the Selling Price is:
SP = MP - (20% of MP) = MP - 0.2 * MP = 0.8 * MP

Setting this equal to the Selling Price we calculated based on profit:
- 0.8 * MP = Rs. 120
- MP = Rs. 120 / 0.8 = Rs. 150

### Step 6: Calculate the Percentage Markup
Now, we can calculate the percentage markup based on the Cost Price (CP) and the Marked Price (MP):
- Markup = MP - CP = Rs. 150 - Rs. 100 = Rs. 50
- Percentage Markup = (Markup / CP) * 100 = (Rs. 50 / Rs. 100) * 100 = 50%

### Final Answer
The percentage markup is **50%**.

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