The marked price of an article is 35% more than its cost price. If a discount of 15% is given, what will be the profit percentage?

The correct answer is $14\frac{3}{4}\%$.

Step-by-Step Explanation:

Step 1: Assume a convenient base Cost Price (CP).
Let the Cost Price (CP) of the article be 100 units.

Step 2: Calculate the Marked Price (MP).
The marked price is 35% more than the cost price.

$\text{MP}=\text{CP}+(35\%\text{of CP})$

$\text{MP}=100+35=135$

Step 3: Calculate the Selling Price (SP) after a 15% discount.
Discount is always calculated on the Marked Price (MP).

$\text{Discount}=15\%\text{of MP}=\frac{15}{100}\times 135=20.25$

Now, calculate the Selling Price:

$\text{SP}=\text{MP}-\text{Discount}$

$\text{SP}=135-20.25=114.75$

Step 4: Calculate the Profit and Profit Percentage.
Profit is the difference between the Selling Price and the Cost Price.

$\text{Profit}=\text{SP}-\text{CP}=114.75-100=14.75$

Since the initial Cost Price was taken as 100, the profit percentage is directly equal to the profit value:

$\text{Profit Percentage}=\frac{\text{Profit}}{\text{CP}}\times 100=\frac{14.75}{100}\times 100=14.75\%$

Converting 14.75% into a mixed fraction:

$14.75\%=14\frac{75}{100}\%=14\frac{3}{4}\%$

Thus, the final profit percentage is $14\frac{3}{4}\%$.