Solving the Shopkeeper’s Pricing Puzzle: A Comprehensive Guide
Understanding the relationship between the marked price, cost price, discount, and selling price is a crucial skill for any shopkeeper. In this article, we will explore a detailed step-by-step guide to solve a common pricing problem, using a practical example. This knowledge will enhance your ability to manage costs, attract customers with competitive pricing, and understand the impact of discounts on profits.
The Problem
A shopkeeper marked the price of an article 25% above the cost price. After allowing a discount of 15% on its marked price, the article was sold at a gain of Rs. 2700. The question is, what is the marked price of the article?
Step-by-Step Solution
Let's denote the cost price (CP) of the article as CP.
1. Calculate the Marked Price (MP)
The shopkeeper marked the price 25% above the cost price. Therefore, the marked price is given by:
MP CP 0.25 times CP 1.25 times CP
2. Calculate the Selling Price (SP)
A discount of 15% is allowed on the marked price. Hence, the selling price can be calculated as follows:
SP MP - 0.15 times MP MP times (1 - 0.15) MP times 0.85
Substituting MP from the previous step:
SP 1.25 times CP times 0.85 1.0625 times CP
3. Relate the Selling Price to the Cost Price
Given that the selling price results in a gain of Rs. 2700:
SP CP 2700
Setting up the equation:
1.0625 times CP CP 2700
Solving for CP:
1.0625 times CP - CP 2700
0.0625 times CP 2700
CP 2700 / 0.0625 43200
4. Calculate the Marked Price
Now we can find the marked price using the cost price:
MP 1.25 times CP 1.25 times 43200 54000
Therefore, the marked price of the article is Rs. 54000.
Alternative Method
Let’s explore another approach using a different set of values to solve the same problem:
Method 2Let the cost price be “C”.
Marked Price (MP) 1.4C
Selling Price (SP) 1 - 0.15 * 1.4C 1.19C
The gain is given by:
SP C Gain
1.19C C 2700
2700 1.19C - C
2700 0.19C
C 2700 / 0.19 400
Therefore, the marked price is:
MP 1.4C 1.4 * 400 560
Another Example
Let the marked price be x Rs.
Discount 0.87x (100 - 13%)
Selling Price 0.87x 1392
87x 139200
x 1600
Hence, the marked price is Rs. 1600.
The marked price can also be calculated as:
Marked price of the article allowed 13% discount 1392 / 87 * 100 Rs. 1600
Generalized Approach
Assume that the original value or cost price was 100.
1. First, it is being increased by 25%. When a value increases by 25%, it becomes 125 (or MRP 125).
2. Second, the value is being reduced by 15%. When a value reduces by 15%, it remains 85% of the original value. The selling price or new value after being reduced is 125 * 85/100 106.25.
This value is 6.25% more than the original value and due to this there is a gain of Rs. 20. Thus, 6.25% corresponds to 20 Rs.
100 or Cost Price 20 * 100 / 6.25 320 Rs.
Conclusion
Understanding the relationship between the marked price, cost price, discount, and selling price is essential for any business. This guide demonstrates how to calculate and keep track of these values to ensure profitability and customer satisfaction. By mastering these calculations, shopkeepers can optimize pricing strategies, maximize profits, and enhance their business operations.