E-commerce
Understanding Gain Percent During Clearance and Marked Price Discounts
Understanding Gain Percent During Clearance and Marked Price Discounts
This article explains how to calculate the gain percent of a shopkeeper during a clearance sale and at the marked price without any discount. Let's explore the concepts with a detailed example.
Example 1: Clearance Sale and Gain Percent
A shopkeeper sells an umbrella for Rs. 300 and gains 20% on the cost price during regular times. However, during a clearance sale, the shopkeeper allows a 10% discount on the marked price. We will calculate the shopkeeper's gain percent during the sale.
Step 1: Determine the Cost Price (CP)
We know that the selling price (SP) of the umbrella is Rs. 300 and the gain is 20% of the cost price (CP).
Formula:
SP CP Gain
Since Gain 20% of CP, we can express it as:
SP CP 0.2 × CP 1.2 × CP
Solving for CP:
300 1.2 × CP
CP 300 / 1.2
CP 250
Step 2: Determine the Marked Price (MP)
During the clearance sale, the shopkeeper sells the umbrella at a 10% discount on the marked price. Let's determine this marked price (MP).
Formula:
SP MP - Discount
Given that the discount is 10% of the marked price, we can write:
SP MP - 0.1 × MP 0.9 × MP
Solving for MP:
300 0.9 × MP
MP 300 / 0.9
MP ≈ 333.33
Step 3: Calculate the Gain During the Sale
Now that we have both the cost price and the selling price during the sale, we can find the gain.
Gain SP - CP
Gain 300 - 250 50
Step 4: Calculate the Gain Percent
The gain percent can be calculated using the formula:
Gain Percent (Gain / CP) × 100
Substituting the values:
Gain Percent (50 / 250) × 100 20%
Thus, the gain percent during the sale is 20%.
Example 2: Selling at Marked Price without Discount
Let's consider another scenario where the marked price of the article is 100. After a 10% discount, the selling price becomes 90. The shopkeeper gains 20% after allowing the discount. We will calculate the shopkeeper's cost price and then find the profit percent if the article is sold at the marked price without any discount.
Step 1: Determine the Cost Price (CP)
Given that the shopkeeper gains 20% after a 10% discount, we can determine the cost price.
Formula:
SP MP - Discount
Where SP 90 and Discount 10% of MP.
SP MP - 0.1 × MP 0.9 × MP
90 0.9 × MP
MP 90 / 0.9 100
Since the shopkeeper gains 20% on the cost price:
SP CP Gain
90 CP 0.2 × CP
90 1.2 × CP
CP 90 / 1.2 75
Step 2: Calculate the Gain if Sold at Marked Price Without Discount
If the article is sold at the marked price of 100, the shopkeeper will earn a profit of 25 (100 - 75).
Step 3: Calculate the Profit Percent
The profit percent can be calculated as follows:
Profit Percent (Profit / Cost Price) × 100
Substituting the values:
Profit Percent (25 / 75) × 100 33.33%
Therefore, the shopkeeper's profit percent if the article is sold at the marked price allowing no discount is 33.33%.
Conclusion
Understanding gain percent during clearance sales and at marked prices without discounts is crucial for shopkeepers to make informed decisions. The examples provided illustrate the step-by-step process of calculating these percentages using the given formulas and data.