The marked price of an article is `20%` more than its cost price . If `5%` discount is given on the marked price , what is the profit per cent ?

Options

A. 5
B. 14
C. 15
D. 25

Answer

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

### Step 1: Determine the Cost Price (CP)
Let's assume the cost price of the article is \( CP = 100 \) (in rupees).

### Step 2: Calculate the Marked Price (MP)
The marked price is 20% more than the cost price. Therefore, we can calculate the marked price as follows:
\[ MP = CP + 20\% \text{ of } CP = 100 + \frac{20}{100} \times 100 = 100 + 20 = 120 \text{ rupees} \]

### Step 3: Calculate the Discount
A discount of 5% is given on the marked price. We can calculate the discount amount as follows:
\[ \text{Discount} = 5\% \text{ of } MP = \frac{5}{100} \times 120 = 6 \text{ rupees} \]

### Step 4: Calculate the Selling Price (SP)
The selling price is the marked price minus the discount:
\[ SP = MP - \text{Discount} = 120 - 6 = 114 \text{ rupees} \]

### Step 5: Calculate the Profit
Profit is calculated as the selling price minus the cost price:
\[ \text{Profit} = SP - CP = 114 - 100 = 14 \text{ rupees} \]

### Step 6: Calculate the Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{14}{100} \right) \times 100 = 14\% \]

### Final Answer
The profit percentage is \( 14\% \).

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