Understanding Profit and Discount Calculation

The problem involves calculating the profit percentage based on the relationship between profit and discount, and the given discount percentage.

Key Information Extraction

• Profit (P) is three times the Discount (D): $ P = 3D $
• Discount Percentage = 6.25%

Calculating Discount and Profit in Terms of Marked Price (MP)

First, convert the discount percentage to a fraction:

$ 6.25\% = \frac{6.25}{100} = \frac{625}{10000} = \frac{1}{16} $

The discount (D) is calculated on the Marked Price (MP):

$ D = \frac{1}{16} \times \text{MP} $

Using the relationship $ P = 3D $, we find the profit (P):

$ P = 3 \times \left( \frac{1}{16} \times \text{MP} \right) = \frac{3}{16} \times \text{MP} $

Determining Selling Price (SP) and Cost Price (CP)

The Selling Price (SP) is the Marked Price (MP) minus the Discount (D):

$ \text{SP} = \text{MP} - D = \text{MP} - \frac{1}{16} \times \text{MP} = \frac{15}{16} \times \text{MP} $

The Selling Price (SP) is also the Cost Price (CP) plus the Profit (P):

$ \text{SP} = \text{CP} + P $

Substitute the expressions for SP and P in terms of MP:

$ \frac{15}{16} \times \text{MP} = \text{CP} + \frac{3}{16} \times \text{MP} $

Now, solve for the Cost Price (CP) in terms of MP:

$ \text{CP} = \frac{15}{16} \times \text{MP} - \frac{3}{16} \times \text{MP} $ $ \text{CP} = \frac{12}{16} \times \text{MP} = \frac{3}{4} \times \text{MP} $

Calculating the Profit Percentage

The profit percentage is calculated using the formula:

$ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 $

Substitute the values of Profit (P) and Cost Price (CP) in terms of MP:

$ \text{Profit Percentage} = \left( \frac{\frac{3}{16} \times \text{MP}}{\frac{3}{4} \times \text{MP}} \right) \times 100 $

Simplify the expression:

$ \text{Profit Percentage} = \left( \frac{3}{16} \times \frac{4}{3} \right) \times 100 $ $ \text{Profit Percentage} = \left( \frac{1}{4} \right) \times 100 $ $ \text{Profit Percentage} = 25\% $