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How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%?
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Understanding the Problem
A shopkeeper wants to set a marked price on his goods such that after giving a discount of 25%, he still makes a profit of 25% over the cost price (c.p).
Key Points to Remember
- Cost Price (c.p): The price at which the shopkeeper buys the goods.
- Marked Price (m.p): The price at which the shopkeeper marks the goods for sale.
- Discount: The reduction from the marked price.
- Selling Price (s.p): The final price after applying the discount.
Calculating Selling Price
- Desired Profit: 25% profit over c.p means:
- Selling Price (s.p) = c.p + 25% of c.p
- s.p = 1.25 * c.p
Applying Discount
- Discount Given: 25% of m.p means:
- s.p = m.p - 25% of m.p
- s.p = 75% of m.p
Setting Up the Equation
To achieve the desired outcome, we set the two equations for s.p equal to each other:
- 1.25 * c.p = 0.75 * m.p
Rearranging the Equation
- m.p = (1.25/0.75) * c.p
- m.p = (5/3) * c.p
- m.p = 1.6667 * c.p
Calculating the Markup Percentage
Now, to find the percentage markup over c.p:
- Markup Percentage = [(m.p - c.p) / c.p] * 100
- Markup Percentage = [(1.6667 * c.p - c.p) / c.p] * 100
- Markup Percentage = (0.6667 * c.p / c.p) * 100 = 66.67%
Final Answer
The shopkeeper should mark his goods 66.67% above the cost price to gain a profit of 25% after allowing a discount of 25% on the marked price.
A shopkeeper wants to set a marked price on his goods such that after giving a discount of 25%, he still makes a profit of 25% over the cost price (c.p).
Key Points to Remember
- Cost Price (c.p): The price at which the shopkeeper buys the goods.
- Marked Price (m.p): The price at which the shopkeeper marks the goods for sale.
- Discount: The reduction from the marked price.
- Selling Price (s.p): The final price after applying the discount.
Calculating Selling Price
- Desired Profit: 25% profit over c.p means:
- Selling Price (s.p) = c.p + 25% of c.p
- s.p = 1.25 * c.p
Applying Discount
- Discount Given: 25% of m.p means:
- s.p = m.p - 25% of m.p
- s.p = 75% of m.p
Setting Up the Equation
To achieve the desired outcome, we set the two equations for s.p equal to each other:
- 1.25 * c.p = 0.75 * m.p
Rearranging the Equation
- m.p = (1.25/0.75) * c.p
- m.p = (5/3) * c.p
- m.p = 1.6667 * c.p
Calculating the Markup Percentage
Now, to find the percentage markup over c.p:
- Markup Percentage = [(m.p - c.p) / c.p] * 100
- Markup Percentage = [(1.6667 * c.p - c.p) / c.p] * 100
- Markup Percentage = (0.6667 * c.p / c.p) * 100 = 66.67%
Final Answer
The shopkeeper should mark his goods 66.67% above the cost price to gain a profit of 25% after allowing a discount of 25% on the marked price.
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How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%?
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How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%?.
How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many percent above the c.p should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 25%?.
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