Calculating Profit after Mark-up and Discount: A Comprehensive Guide for SEO
Understanding how to calculate profit after applying a mark-up and then giving a discount is a fundamental concept in retail and business management. This guide will walk you through the step-by-step process, using examples and practical applications to help you master this calculation.
The Problem Statement
A shopkeeper bought an article for Rs 12,000. He marked the price 25% above the cost price. If during selling a discount of 10% is given on the marked price, what is the profit or loss incurred by the shopkeeper?
A Step-by-Step Solution
Given
Cost price (CP) Rs 12,000
Mark-up
Mark-up 25% of CP 25/100 * 12,000
Marked price (MP) CP Mark-up 12,000 25/100 * 12,000
MP 12,000 3,000 Rs 15,000
Selling Price after Discount
Discount 10% of MP 10/100 * 15,000
Discount 1,500
Selling price (SP) MP - Discount 15,000 - 1,500
SP Rs 13,500
Calculation of Profit
Profit SP - CP 13,500 - 12,000
Profit Rs 1,500
Profit percentage (Profit / CP) * 100 (1,500 / 12,000) * 100
Profit percentage 12.5%
Special Cases
Example 1
Suppose the cost price of the item is Rs 100.
Marked price of the item 100 20% of 100 100 20 Rs 120
Discount on the marked price 10% of 120 10/100 * 120 12
Sale price 120 - 12 Rs 108
Profit Sale price - Cost price 108 - 100
Profit Rs 8
Example 2
Let the cost price of the goods be Rs x.
Marked price x 20% of x x 0.2x 1.2x
Selling price 1.2x - 10% of 1.2x 1.2x - 0.12x 1.08x
Gain 1.08x - x 0.08x
Gain percentage (0.08x / x) * 100 8%
Example 3
Cost price be Rs 10.
Marked price 10 20% of 10 10 2 12
10% discount 12 * 10/100 1.2
Selling price 12 - 1.2 10.8
Profit 10.8 - 10 0.8
Profit percentage (0.8 / 10) * 100 8%
General Case
Let the cost price of the article be Rs 100.
Marked price at 20% above the cost price 120
Discount at 10% 120 * 10/100 12
Selling price after discount 120 - 12 108
Profit Selling price - Cost price 108 - 100 8
Profit percentage (8 / 100) * 100 8%
Conclusion
We can see that the profit percentage is consistently 8% in all scenarios where the mark-up and discount conditions remain the same. Understanding this concept can help shopkeepers and business owners in making informed decisions about pricing and sales strategies.