A manufacturer sells an article at p% more than the cost of production. If he gives a discount of q% to the customer, find the profit in percentage.

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Points to Remember:

  • The question involves calculating profit percentage after a discount is applied to a marked-up price.
  • The solution requires understanding percentage calculations and profit/loss concepts.
  • The final answer will be an expression in terms of p and q.

Introduction:

This question deals with a common business scenario: calculating profit after offering a discount. A manufacturer sets a selling price by adding a markup percentage (p%) to the cost of production. However, to attract customers, a discount (q%) is often offered. This necessitates calculating the final profit percentage considering both the markup and the discount. Understanding this calculation is crucial for businesses to determine optimal pricing strategies and ensure profitability.

Body:

1. Defining Variables and Setting up the Equation:

Let’s assume the cost of production of the article is ‘C’.

  • The manufacturer sells the article at p% more than the cost of production. Therefore, the selling price before discount (SPbefore) is: C + (p/100)C = C(1 + p/100)

  • A discount of q% is given to the customer. The selling price after discount (SPafter) is: C(1 + p/100) – (q/100) * C(1 + p/100) = C(1 + p/100)(1 – q/100)

2. Calculating the Profit:

Profit = Selling Price after discount – Cost Price = C(1 + p/100)(1 – q/100) – C

3. Calculating the Profit Percentage:

Profit Percentage = (Profit / Cost Price) * 100 = [C(1 + p/100)(1 – q/100) – C] / C * 100

Simplifying the expression:

Profit Percentage = [(1 + p/100)(1 – q/100) – 1] * 100

Profit Percentage = [1 + p/100 – q/100 – pq/10000 – 1] * 100

Profit Percentage = (p/100 – q/100 – pq/10000) * 100

Profit Percentage = p – q – pq/100

4. Illustrative Example:

Let’s say the cost of production (C) is $100, p = 20% and q = 10%.

  • SPbefore = 100(1 + 20/100) = $120
  • SPafter = 120(1 – 10/100) = $108
  • Profit = 108 – 100 = $8
  • Profit Percentage = (8/100) * 100 = 8%

Using the formula derived above: Profit Percentage = 20 – 10 – (20*10)/100 = 8%

Conclusion:

The profit percentage after a discount is given by the formula: p – q – pq/100, where ‘p’ is the markup percentage and ‘q’ is the discount percentage. This formula provides a concise and efficient way to calculate the final profit, considering both the markup and the discount offered. Businesses can utilize this formula to strategically manage their pricing, ensuring profitability while remaining competitive. Understanding the interplay between markup and discounts is essential for sustainable business growth and efficient resource allocation. A holistic approach to pricing, considering market dynamics and customer preferences, is crucial for long-term success.

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