Calculating Shopkeeper's Gain Percentage with Markup and Discount

This problem involves calculating the net gain percentage when a shopkeeper first increases the cost price to mark the article and then offers a discount on the marked price.

Let's define some key terms used in this calculation:

• Cost Price (CP): The original price at which the shopkeeper buys the article.
• Marked Price (MP): The price displayed on the article after increasing the cost price.
• Selling Price (SP): The final price at which the shopkeeper sells the article after giving a discount on the marked price.
• Markup Percentage: The percentage increase from CP to MP.
• Discount Percentage: The percentage reduction offered on MP to arrive at SP.
• Gain (or Profit): The difference between Selling Price and Cost Price (\(SP - CP\)) when \(SP > CP\).
• Gain Percentage: Calculated as \(\frac{\text{Gain}}{\text{CP}} \times 100\).

Step-by-Step Gain Percentage Calculation

To solve this problem, we can assume a base Cost Price for the article. Let's assume the Cost Price (CP) of the article is Rs. 100.

1. Calculate the Marked Price (MP):

   The shopkeeper marks up the article by 20% of the Cost Price.

   Markup amount = 20% of CP

   Markup amount = \(\frac{20}{100} \times 100 = \text{Rs. } 20\)

   Marked Price (MP) = CP + Markup amount

   MP = \(\text{Rs. } 100 + \text{Rs. } 20 = \text{Rs. } 120\)

   So, the Marked Price is Rs. 120.

2. Calculate the Selling Price (SP):

   The shopkeeper offers a discount of 10% on the Marked Price.

   Discount amount = 10% of MP

   Discount amount = \(\frac{10}{100} \times 120 = \frac{1}{10} \times 120 = \text{Rs. } 12\)

   Selling Price (SP) = MP - Discount amount

   SP = \(\text{Rs. } 120 - \text{Rs. } 12 = \text{Rs. } 108\)

   So, the Selling Price is Rs. 108.

3. Calculate the Gain:

   Gain = Selling Price (SP) - Cost Price (CP)

   Gain = \(\text{Rs. } 108 - \text{Rs. } 100 = \text{Rs. } 8\)

   Since SP > CP, there is a gain of Rs. 8.

4. Calculate the Gain Percentage:

   Gain Percentage = \(\frac{\text{Gain}}{\text{CP}} \times 100\)

   Gain Percentage = \(\frac{8}{100} \times 100 = 8\%\)

The shopkeeper's gain percentage is 8%.

Summary of Price Calculations

Revision Table: Key Concepts for Profit and Loss

Additional Information on Gain Percentage Calculation

Understanding the relationship between Cost Price, Marked Price, and Selling Price is crucial for solving such problems. The markup is always calculated on the Cost Price, leading to the Marked Price. The discount is always calculated on the Marked Price, leading to the Selling Price. The final gain or loss is always calculated by comparing the Selling Price and the Cost Price.

In this specific problem, the shopkeeper used the markup to create room for offering a discount while still making a profit. Even though a 10% discount is given, the initial 20% markup is high enough to ensure a net gain.

Another way to approach this type of problem is using successive percentages, but the step-by-step method shown above is often clearer for understanding the flow from CP to MP to SP and finally to gain percentage.

Always remember that profit/loss percentage is calculated on the Cost Price unless explicitly stated otherwise, while discount percentage is calculated on the Marked Price.