Question

A shopkeeper marks an article 25% above the cost price and gives a discount of 10%. His profit percentage is:

• A. 10%
• B. 11.5%
• C. 12.5%
• D. 15%

Hint:

Whenever a markup and a discount are applied sequentially, skip assuming values and use the direct change formula: $\text{Profit}% = M - D - \frac{M \times D}{100}$. Plugging in $M = 25$ and $D = 10$: $$\text{Profit}% = 25 - 10 - \frac{25 \times 10}{100} = 15 - 2.5 = 12.5%$$ This gives you the exact matching result in a single text step!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Profit or loss percentage is fundamentally computed relative to the Cost Price ($CP$). The Marked Price ($MP$) represents an increased price level set by a retailer above the cost price using a markup factor. The final Selling Price ($SP$) is determined by applying a percentage discount subtraction directly to that marked price level.

Step 2: Key Formula or Approach:
1. $MP = CP \times \left(1 + \frac{\text{Markup}%}{100}\right)$
2. $SP = MP \times \left(1 - \frac{\text{Discount}%}{100}\right)$
3. $\text{Profit}% = \left(\frac{SP - CP}{CP}\right) \times 100%$
Alternatively, because the adjustments take place one after another on the base value, we can utilize the successive net percentage conversion relationship: $$\text{Net Profit}% = M - D - \frac{M \times D}{100}$$ where $M$ is the markup percentage and $D$ is the discount percentage.

Step 3: Detailed Explanation:
Let's assume the base Cost Price ($CP$) of the article is ₹$100$ to simplify calculations: Find the Marked Price ($MP$): The shopkeeper increases the price tag by $25%$ over the cost price. $$MP = 100 + (25% \text{ of } 100) = 100 + 25 = \text{₹}125$$ Find the Selling Price ($SP$): A $10%$ discount reduction is applied directly to the marked value. $$\text{Discount Amount} = 10% \text{ of } 125 = \frac{10}{100} \times 125 = \text{₹}12.5$$ $$SP = MP - \text{Discount Amount} = 125 - 12.5 = \text{₹}112.5$$ Find the Overall Profit Percentage: $$\text{Profit Value} = SP - CP = 112.5 - 100 = \text{₹}12.5$$ $$\text{Profit}% = \left(\frac{12.5}{100}\right) \times 100 = 12.5%$$

Step 4: Final Answer:
His profit percentage is 12.5%.