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?

To solve this problem, let's define some variables and use the given information step-by-step:

1. **Define Variables**:
   - Let \( x \) be the number of articles of type A in the first lot.
   - Let \( y \) 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 \( C \).

2. **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 \( 1.5(x + y) \).
   - It’s also given that the number of articles of A in the first lot (\( x \)) is equal to the number of articles of B in the second lot.

3. **Calculate Selling Prices**:
   - Since the cost price per article for both A and B is \( C \):
     - Selling price of each article of type B is \( 0.95C \) (since it is sold at a 5% loss).
     - Let the selling price of each article of type A be \( S_A \), which we need to find to determine the profit on A.

4. **Total Cost Price and Total Selling Price**:
   - **Total Cost Price (TCP)** for both lots:
     \[
     \text{TCP} = (x + y)C + \left(x + 1.5y\right)C = \left(2x + 2.5y\right)C
     \]
   - **Total Selling Price (TSP)**:
     - Selling price for type B is \( y \times 0.95C \) (from the first lot) and \( 1.5y \times 0.95C \) (from the second lot):
       \[
       \text{TSP for B} = (y + 1.5y) \times 0.95C = 2.5y \times 0.95C = 2.375yC
       \]
     - Selling price for type A is \( x \times S_A + x \times S_A = 2xS_A \).

   - Therefore, the total selling price is:
     \[
     \text{TSP} = 2xS_A + 2.375yC
     \]

5. **Overall Profit Calculation**:


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?

Explore a profit and loss problem where a retailer buys two types of articles in two lots, sells one at a loss of 5%, and aims for an overall profit of 10%. Learn how to find the profit percentage for the other article using algebraic equations. Suitable for Grades 10-12 students.

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