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Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.
solve using formulae?
solve using formulae?
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Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20...
Understanding the Problem
Ramesh bought two boxes for a total of Rs 1300. He sold one box at a profit of 20% and the other at a loss of 12%. The selling prices of both boxes are the same. We need to find the cost price of each box.
Let’s Define Variables
- Let the cost price of the first box be Rs x.
- Let the cost price of the second box be Rs (1300 - x).
Calculating Selling Prices
- Selling price of the first box (SP1):
- SP1 = Cost Price + Profit
- SP1 = x + 20% of x = x + (20/100)x = 1.2x
- Selling price of the second box (SP2):
- SP2 = Cost Price - Loss
- SP2 = (1300 - x) - 12% of (1300 - x)
- SP2 = (1300 - x) - (12/100)(1300 - x) = (1300 - x) - 0.12(1300 - x)
- SP2 = (1300 - x)(1 - 0.12) = (1300 - x)(0.88)
Setting Selling Prices Equal
Since the selling prices are the same:
1.2x = 0.88(1300 - x)
Solving for x
- Expand the equation:
1.2x = 0.88 * 1300 - 0.88x
- Combine like terms:
1.2x + 0.88x = 0.88 * 1300
- Simplify:
2.08x = 0.88 * 1300
- Calculate:
x = (0.88 * 1300) / 2.08
- Calculate x:
x = 520
Cost Prices of Each Box
- Cost price of the first box (CP1): Rs 520
- Cost price of the second box (CP2): Rs 1300 - Rs 520 = Rs 780
Conclusion
The cost prices of the boxes are Rs 520 and Rs 780, respectively.
Ramesh bought two boxes for a total of Rs 1300. He sold one box at a profit of 20% and the other at a loss of 12%. The selling prices of both boxes are the same. We need to find the cost price of each box.
Let’s Define Variables
- Let the cost price of the first box be Rs x.
- Let the cost price of the second box be Rs (1300 - x).
Calculating Selling Prices
- Selling price of the first box (SP1):
- SP1 = Cost Price + Profit
- SP1 = x + 20% of x = x + (20/100)x = 1.2x
- Selling price of the second box (SP2):
- SP2 = Cost Price - Loss
- SP2 = (1300 - x) - 12% of (1300 - x)
- SP2 = (1300 - x) - (12/100)(1300 - x) = (1300 - x) - 0.12(1300 - x)
- SP2 = (1300 - x)(1 - 0.12) = (1300 - x)(0.88)
Setting Selling Prices Equal
Since the selling prices are the same:
1.2x = 0.88(1300 - x)
Solving for x
- Expand the equation:
1.2x = 0.88 * 1300 - 0.88x
- Combine like terms:
1.2x + 0.88x = 0.88 * 1300
- Simplify:
2.08x = 0.88 * 1300
- Calculate:
x = (0.88 * 1300) / 2.08
- Calculate x:
x = 520
Cost Prices of Each Box
- Cost price of the first box (CP1): Rs 520
- Cost price of the second box (CP2): Rs 1300 - Rs 520 = Rs 780
Conclusion
The cost prices of the boxes are Rs 520 and Rs 780, respectively.
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Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.solve using formulae?
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Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.solve using formulae? 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 Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.solve using formulae? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.solve using formulae?.
Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.solve using formulae? 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 Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.solve using formulae? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both boxes is the same, find the cost price of each box.solve using formulae?.
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