Understanding Market Price, Cost Price, and Discount

This problem involves calculating the final gain percentage on a product (a bedsheet) after considering its cost price, a markup to determine the market price, and a subsequent discount offered on the market price.

• Cost Price (CP): The original price the seller paid for the bedsheet.
• Market Price (MP): The price displayed for the bedsheet, which includes a markup over the cost price.
• Selling Price (SP): The actual price at which the bedsheet is sold after applying a discount to the market price.
• Gain Percentage: The profit expressed as a percentage of the cost price.

Step-by-Step Calculation of Gain Percentage

Let's assume the Cost Price (CP) of the bedsheet is $100$. This makes calculations easier.

1. Calculate the Market Price (MP):

   The market price is 24% above the cost price.
   MP = CP + (24% of CP)
   MP = CP \times (1 + \frac{24}{100})
   MP = CP \times (1 + 0.24)
   MP = 1.24 \times CP

   If CP = $100$, then MP = $1.24 \times 100 = $124$.

2. Calculate the Selling Price (SP):

   A discount of 15% is declared on the market price.
   SP = MP - (15% of MP)
   SP = MP \times (1 - \frac{15}{100})
   SP = MP \times (1 - 0.15)
   SP = 0.85 \times MP

   Substituting the value of MP:

   SP = 0.85 \times (1.24 \times CP)

   SP = 1.054 \times CP

   If MP = $124$, then SP = $0.85 \times 124 = $105.40$.

3. Calculate the Gain:

   Gain = SP - CP
   Gain = (1.054 \times CP) - CP
   Gain = CP \times (1.054 - 1)
   Gain = 0.054 \times CP

   If CP = $100$ and SP = $105.40$, then Gain = $105.40 - 100 = $5.40$.

4. Calculate the Gain Percentage:

   Gain Percentage = (\frac{Gain}{CP}) \times 100
   Gain Percentage = (\frac{0.054 \times CP}{CP}) \times 100
   Gain Percentage = 0.054 \times 100
   Gain Percentage = 5.4%

Final Gain Percentage Result

The overall gain percentage achieved after marking up the cost price and then applying the discount is 5.40%.