The marked price of an article is 40% more than its cost price. If 25% discount is given, what will be the profit per cent ?

Options

A. `12.5`
B. 10
C. 15
D. 5

Answer

To solve the problem step-by-step, we need to find the profit percentage given that the marked price (MP) of an article is 40% more than its cost price (CP) and that a discount of 25% is applied to the marked price.

### Step 1: Define the Cost Price (CP)
Let's assume the cost price (CP) of the article is \( x \).

### Step 2: Calculate the Marked Price (MP)
The marked price (MP) is 40% more than the cost price. Therefore, we can calculate the marked price as follows:
\[ MP = CP + 40\% \text{ of } CP = x + 0.4x = 1.4x \]

### Step 3: Calculate the Selling Price (SP) after Discount
A discount of 25% is given on the marked price. The selling price (SP) can be calculated as:
\[ SP = MP - 25\% \text{ of } MP = MP - 0.25 \times MP = MP \times (1 - 0.25) = MP \times 0.75 \]
Substituting the value of MP:
\[ SP = 1.4x \times 0.75 = 1.05x \]

### Step 4: Calculate the Profit
Profit is calculated as the difference between the selling price (SP) and the cost price (CP):
\[ \text{Profit} = SP - CP = 1.05x - x = 0.05x \]

### Step 5: Calculate the Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{0.05x}{x} \right) \times 100 = 5\% \]

### Final Answer
The profit percentage is **5%**.

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