The marked price of an article is 40% more than its cost price. If 10% discount is given, then what is the profit percentage?

Options

A. 10
B. 20
C. 26
D. 32

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Cost Price (CP)
Let the cost price (CP) of the article be \( x \).

### 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 10% is given on the marked price. Thus, the selling price (SP) can be calculated as:
\[ SP = MP - 10\% \text{ of } MP = MP - 0.1 \times MP = MP \times (1 - 0.1) = 0.9 \times MP \]
Substituting the value of MP:
\[ SP = 0.9 \times 1.4x = 1.26x \]

### Step 4: Calculate the Profit
Profit is defined as the selling price minus the cost price:
\[ \text{Profit} = SP - CP = 1.26x - x = 0.26x \]

### 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:
\[ \text{Profit Percentage} = \left( \frac{0.26x}{x} \right) \times 100 = 26\% \]

### Conclusion
The profit percentage is \( 26\% \).