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
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
