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A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price?
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A person sold his article at 20% profit. If he purchase it at 1000 les...
Understanding the Problem
To find the original cost price of the article, let's denote:
- CP = Original Cost Price
- SP1 = Selling Price with 20% profit
- SP2 = Selling Price with 30% more profit
Initial Scenario
- Given a 20% profit, the selling price can be expressed as:
SP1 = CP + 0.20 * CP = 1.20 * CP
Modified Scenario
- If the cost price is reduced by 1000, the new cost price becomes:
New CP = CP - 1000
- The selling price increases by 200, leading to:
SP2 = SP1 + 200 = 1.20 * CP + 200
- The profit in this scenario is 30% more than the original profit. Thus, the new selling price can also be expressed as:
SP2 = New CP + 0.30 * New CP
SP2 = (CP - 1000) + 0.30 * (CP - 1000)
SP2 = 1.30 * (CP - 1000)
Setting Up the Equation
Now, equate the two expressions for SP2:
1.20 * CP + 200 = 1.30 * (CP - 1000)
Solving the Equation
1. Distribute on the right side:
1.20 * CP + 200 = 1.30 * CP - 1300
2. Rearranging gives:
1300 + 200 = 1.30 * CP - 1.20 * CP
1500 = 0.10 * CP
3. Solving for CP:
CP = 1500 / 0.10
CP = 15000
Conclusion
The original cost price of the article is 15000.
To find the original cost price of the article, let's denote:
- CP = Original Cost Price
- SP1 = Selling Price with 20% profit
- SP2 = Selling Price with 30% more profit
Initial Scenario
- Given a 20% profit, the selling price can be expressed as:
SP1 = CP + 0.20 * CP = 1.20 * CP
Modified Scenario
- If the cost price is reduced by 1000, the new cost price becomes:
New CP = CP - 1000
- The selling price increases by 200, leading to:
SP2 = SP1 + 200 = 1.20 * CP + 200
- The profit in this scenario is 30% more than the original profit. Thus, the new selling price can also be expressed as:
SP2 = New CP + 0.30 * New CP
SP2 = (CP - 1000) + 0.30 * (CP - 1000)
SP2 = 1.30 * (CP - 1000)
Setting Up the Equation
Now, equate the two expressions for SP2:
1.20 * CP + 200 = 1.30 * (CP - 1000)
Solving the Equation
1. Distribute on the right side:
1.20 * CP + 200 = 1.30 * CP - 1300
2. Rearranging gives:
1300 + 200 = 1.30 * CP - 1.20 * CP
1500 = 0.10 * CP
3. Solving for CP:
CP = 1500 / 0.10
CP = 15000
Conclusion
The original cost price of the article is 15000.
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A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price?
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A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price?.
A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person sold his article at 20% profit. If he purchase it at 1000 less and sold it 200 more price then he gain 30% more profit. Find the original cost price?.
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