The marked price of an article is 160 percent of the cost price. If 20 percent discount is given, then what will be the profit percentage?
28 percent
Understanding Profit Percentage with Marked Price and Discount
This problem involves calculating the profit percentage on an article when its marked price is set as a certain percentage of the cost price and a discount is offered on the marked price. To solve this, we need to understand the relationships between Cost Price (CP), Marked Price (MP), Selling Price (SP), Discount, and Profit.
- Cost Price (CP): The price at which the article is bought.
- Marked Price (MP): The price listed on the article, often higher than the cost price.
- Discount: A reduction offered on the Marked Price.
- Selling Price (SP): The price at which the article is sold after the discount (if any).
- Profit: The difference between the Selling Price and the Cost Price (SP - CP), when SP > CP.
- Profit Percentage: Calculated as $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$.
Calculating Profit Percentage Step-by-Step
Let's assume a base value for the Cost Price (CP) to make calculations easier. A common practice is to assume CP = ₹100.
- Calculate the Marked Price (MP):
The problem states the marked price is 160 percent of the cost price.
MP = 160% of CP
MP = $\frac{160}{100} \times \text{CP}$
Assuming CP = ₹100:
MP = $\frac{160}{100} \times 100 = \text{₹}160$
- Calculate the Discount Amount:
A 20 percent discount is given on the marked price.
Discount = 20% of MP
Discount = $\frac{20}{100} \times \text{MP}$
Using the calculated MP = ₹160:
Discount = $\frac{20}{100} \times 160 = \frac{1}{5} \times 160 = \text{₹}32$
- Calculate the Selling Price (SP):
The selling price is the marked price minus the discount.
SP = MP - Discount
SP = $160 - 32 = \text{₹}128$
- Calculate the Profit:
Profit is the difference between the selling price and the cost price.
Profit = SP - CP
Assuming CP = ₹100 and calculated SP = ₹128:
Profit = $128 - 100 = \text{₹}28$
- Calculate the Profit Percentage:
Profit percentage is calculated on the cost price.
Profit Percentage = $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$
Using Profit = ₹28 and CP = ₹100:
Profit Percentage = $\left( \frac{28}{100} \right) \times 100 = 28$ percent
So, the profit percentage is 28 percent.
Summary of Calculations
| Item | Value (assuming CP = ₹100) | Calculation |
|---|---|---|
| Cost Price (CP) | ₹100 | Assumed |
| Marked Price (MP) | ₹160 | 160% of CP = $1.60 \times 100$ |
| Discount Amount | ₹32 | 20% of MP = $0.20 \times 160$ |
| Selling Price (SP) | ₹128 | MP - Discount = $160 - 32$ |
| Profit | ₹28 | SP - CP = $128 - 100$ |
| Profit Percentage | 28% | $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 = \left( \frac{28}{100} \right) \times 100$ |
Conclusion on Profit Calculation
Based on the calculations, if the marked price of an article is 160 percent of the cost price and a 20 percent discount is given on the marked price, the resulting profit percentage will be 28 percent.
Revision Table: Key Formulas
| Concept | Formula |
|---|---|
| Marked Price (MP) from CP and percentage increase | MP = CP $\times$ (1 + Percentage Increase / 100) |
| Discount Amount | Discount = Discount Percentage $\times$ MP |
| Selling Price (SP) with Discount | SP = MP - Discount |
| Profit | Profit = SP - CP (if SP > CP) |
| Loss | Loss = CP - SP (if CP > SP) |
| Profit Percentage | Profit % = $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$ |
| Loss Percentage | Loss % = $\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100$ |
Additional Information: Relation between CP, MP, SP, Discount, and Profit
Understanding the flow from cost price to selling price via marked price and discount is crucial in profit and loss problems. The seller first decides the cost price, then marks up the price to set the marked price (often considering potential discounts). Finally, a discount might be offered on the marked price to arrive at the selling price. The profit or loss is determined by comparing this final selling price with the initial cost price.
- When MP > CP, there is a markup.
- Discount is always calculated on the MP.
- Profit/Loss is always calculated on the CP.
These concepts are fundamental in commercial arithmetic and frequently appear in various exams. Practicing different scenarios involving these variables helps solidify understanding.
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
