Step 1: Understanding the Concept:
Profit and loss calculations in retail involve three distinct price levels: the Cost Price (CP), the Marked Price (MP), and the Selling Price (SP).
The Cost Price is the original price at which the shopkeeper purchases the item.
The Marked Price is the price the shopkeeper "tags" on the item after adding a "markup." This is usually done to provide a cushion for offering discounts while still maintaining a profit margin.
The Discount is a percentage reduction offered specifically on the Marked Price. It is a common mistake to calculate the discount on the cost price; it must always be applied to the MP.
The final price after the discount is the Selling Price. If the SP is higher than the CP, a profit is made. The profit percentage is always calculated relative to the original Cost Price.
Step 2: Key Formula or Approach:
We can solve this using two main methods:
1. The Assumption Method: Assume CP is 100 to simplify the percentage calculations.
2. The Successive Percentage Formula: Since the markup and discount are applied one after the other on the same base, we can use:
\[ \text{Net Profit%} = M - D - \frac{M \times D}{100} \]
where \(M\) is the Markup % and \(D\) is the Discount %.
Step 3: Detailed Explanation:
Let's use the assumption method to see the flow of money clearly.
Assume the base Cost Price (CP) of the article is \(100\).
First, the shopkeeper increases the price by 25% over the CP to set the Marked Price.
\[ \text{Markup Amount} = 25% \text{ of } 100 = 25 \]
\[ \text{Marked Price (MP)} = CP + \text{Markup} = 100 + 25 = 125 \]
Now, a 10% discount is offered on this new tag price of 125.
\[ \text{Discount Amount} = 10% \text{ of } 125 = \frac{10}{100} \times 125 = 12.5 \]
The Selling Price (SP) is the amount the customer actually pays after the discount is removed from the MP.
\[ \text{SP} = \text{MP} - \text{Discount Amount} = 125 - 12.5 = 112.5 \]
Now, we compare the final Selling Price to the original Cost Price to find the profit.
\[ \text{Profit Value} = \text{SP} - \text{CP} = 112.5 - 100 = 12.5 \]
Since we assumed the CP to be 100, this numerical difference of 12.5 represents exactly 12.5% of the CP.
\[ \text{Profit%} = \left( \frac{12.5}{100} \right) \times 100 = 12.5% \]
Step 4: Final Answer:
The shopkeeper's overall profit percentage is 12.5%, which is option (c).