Calculating Discount Percentage for a Target Gain
To find the required discount percentage, we need to determine the relationship between the cost price (\(CP\)), marked price (\(MP\)), and the selling price (\(SP\)) needed for a specific gain.
Step 1: Assume Cost Price and Calculate Marked Price
Let the Cost Price (\(CP\)) of the item be \(100\).
The shopkeeper fixes the Marked Price (\(MP\)) 20% above the cost price:
\( MP = CP + (20\% \text{ of } CP) \)
\( MP = 100 + (0.20 \times 100) = 100 + 20 = 120 \)
So, the Marked Price is \(120\).
Step 2: Calculate the Selling Price for the Desired Gain
The shopkeeper aims for a gain of 2%.
The required Selling Price (\(SP\)) is calculated on the cost price:
\( SP = CP + (2\% \text{ of } CP) \)
\( SP = 100 + (0.02 \times 100) = 100 + 2 = 102 \)
The target Selling Price is \(102\).
Step 3: Calculate the Discount Amount
The discount is the difference between the Marked Price and the Selling Price.
\( \text{Discount Amount} = MP - SP \)
\( \text{Discount Amount} = 120 - 102 = 18 \)
The discount amount is \(18\).
Step 4: Calculate the Discount Percentage
The Discount Percentage is calculated based on the Marked Price.
\( \text{Discount Percentage} = \left( \frac{\text{Discount Amount}}{MP} \right) \times 100 \% \)
\( \text{Discount Percentage} = \left( \frac{18}{120} \right) \times 100 \% \)
\( \text{Discount Percentage} = \left( \frac{3}{20} \right) \times 100 \% = 15\% \)
Therefore, the shopkeeper should offer a 15% discount.
Similar Questions
A trader marks an article 25% above its cost price. He allows a discount of 10% on the marked price. After giving the discount, he makes a profit of ₹180 on the article. What is the cost price of the article?
A shopkeeper marks a product 75% above cost price and offers two successive discounts of 30% and 40%. What is the profit or loss percentage?
A trader buys 187 pens at ₹23 each. During transportation, 7 pens get damaged and cannot be sold. He sells the remaining pens at ₹27 each. Find his profit percentage. (rounded off to one decimal place)
A dealer buys a table for ₹2,750. He first marks it up by 28%, then allows a 12% discount to a customer. If the customer also pays 5% GST on the selling price, find the profit percentage (excluding GST) made by the dealer.
- During a sale, 50% of the goods are sold at a 49% profit, 32% of the remaining goods are sold at a 45% profit and the still remaining goods are sold at a loss of 15%. If there is an overall profit of x%, then what is the value of x?
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- The rate of discount on an article whose marked price is ₹ 170 and selling price is ₹ 130 is:
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?
