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A man sold a sofa at a gain of 15 percent had he sold it for ₹340less he would have lost 2 percent at what price did he purchase it?
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A man sold a sofa at a gain of 15 percent had he sold it for ₹340less ...
Problem Overview
A man sold a sofa at a gain of 15%. However, had he sold it for ₹340 less, he would have incurred a loss of 2%. We need to find the purchase price of the sofa.
Let’s Define Variables
- Let the cost price (CP) of the sofa be ₹x.
- Selling Price (SP) with a gain of 15% can be calculated as:
- SP = CP + 15% of CP = x + 0.15x = 1.15x
Finding the Selling Price with Loss
- If he sold the sofa for ₹340 less, the selling price would be:
- SP with loss = 1.15x - 340
- According to the problem, with this selling price, he would incur a loss of 2%, which can be represented as:
- SP with loss = CP - 2% of CP = x - 0.02x = 0.98x
Setting Up the Equation
Now, we equate the two expressions for selling price:
- 1.15x - 340 = 0.98x
Simplifying the Equation
1. Rearranging gives:
- 1.15x - 0.98x = 340
- 0.17x = 340
2. Solving for x:
- x = 340 / 0.17
- x = ₹2000
Conclusion
The man purchased the sofa for ₹2000.
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A man sold a sofa at a gain of 15 percent had he sold it for ₹340less he would have lost 2 percent at what price did he purchase it?
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A man sold a sofa at a gain of 15 percent had he sold it for ₹340less he would have lost 2 percent at what price did he purchase it? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A man sold a sofa at a gain of 15 percent had he sold it for ₹340less he would have lost 2 percent at what price did he purchase it? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man sold a sofa at a gain of 15 percent had he sold it for ₹340less he would have lost 2 percent at what price did he purchase it?.
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