Math Problem Statement
A retailer buys two types of articles - A and B - in two lots from the wholesaler. The second lot has 50% more articles than the first lot. Number of articles of A in the first lot is equal to the
number of articles of B in the second lot. The cost prices of articles A and B are equal and he sells article B at a loss of 5%. If the overall profit is 10%, what is the profit percentage from
the sale of article A?
Solution
To solve this problem, let's define some variables and use the given information step-by-step:
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Define Variables:
- Let be the number of articles of type A in the first lot.
- Let be the number of articles of type B in the first lot.
- The cost price per article for both A and B is the same. Let this be .
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Relate the Number of Articles in the Lots:
- The second lot has 50% more articles than the first lot, so the total number of articles in the second lot is .
- It’s also given that the number of articles of A in the first lot () is equal to the number of articles of B in the second lot.
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Calculate Selling Prices:
- Since the cost price per article for both A and B is :
- Selling price of each article of type B is (since it is sold at a 5% loss).
- Let the selling price of each article of type A be , which we need to find to determine the profit on A.
- Since the cost price per article for both A and B is :
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Total Cost Price and Total Selling Price:
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Total Cost Price (TCP) for both lots:
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Total Selling Price (TSP):
- Selling price for type B is (from the first lot) and (from the second lot):
- Selling price for type A is .
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Therefore, the total selling price is:
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Overall Profit Calculation:
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Math Problem Analysis
Mathematical Concepts
Algebra
Profit and Loss
Equations
Formulas
Total Cost Price (TCP) = (x + y)C + (x + 1.5y)C = (2x + 2.5y)C
Total Selling Price (TSP) for B = (y + 1.5y) × 0.95C = 2.375yC
Overall Profit Percentage = (TSP - TCP) / TCP × 100%
Theorems
Profit and Loss Theorem
Suitable Grade Level
Grades 10-12