Understanding the Trader's Profit Calculation

This problem involves calculating the final profit percentage for a trader who applies a markup to the cost price and then offers a discount on the marked price.

Key Concepts:

• Cost Price (CP): The original price the trader paid for the article.
• Marked Price (MP): The price the trader sets for the article, which is higher than the CP.
• Discount: A reduction in price offered on the Marked Price.
• Selling Price (SP): The final price at which the article is sold after the discount.
• Profit: The difference between the Selling Price and the Cost Price (SP - CP).
• Profit Percentage: The profit expressed as a percentage of the Cost Price, calculated as (\frac{Profit}{CP}) \times 100\%.

Step-by-Step Calculation

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

Step 1: Calculate the Marked Price (MP)

The trader marks the price 50 percent more than the cost price.

Markup Amount = 50% of CP

Markup Amount = 0.50 \times \$100 = \$50

Marked Price (MP) = CP + Markup Amount

MP = \$100 + \$50 = \$150

Step 2: Calculate the Discount Amount

The trader allows a discount of 30 percent on the Marked Price.

Discount Amount = 30% of MP

Discount Amount = 0.30 \times \$150

Discount Amount = \$45

Step 3: Calculate the Selling Price (SP)

The Selling Price is the Marked Price minus the Discount Amount.

Selling Price (SP) = MP - Discount Amount

SP = \$150 - \$45 = \$105

Step 4: Calculate the Profit

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

Profit = \$105 - \$100 = \$5

Step 5: Calculate the Profit Percentage

Profit Percentage = (\frac{Profit}{CP}) \times 100\%

Profit Percentage = (\frac{\$5}{\$100}) \times 100\%

Profit Percentage = 0.05 \times 100\% = 5\%

Conclusion

After marking the price 50 percent above the cost price and then allowing a 30 percent discount, the trader makes a profit of 5 percent.