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:

  1. Define Variables:

    • Let xx be the number of articles of type A in the first lot.
    • Let yy 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 CC.
  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)1.5(x + y).
    • It’s also given that the number of articles of A in the first lot (xx) 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 CC:
      • Selling price of each article of type B is 0.95C0.95C (since it is sold at a 5% loss).
      • Let the selling price of each article of type A be SAS_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: TCP=(x+y)C+(x+1.5y)C=(2x+2.5y)C\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×0.95Cy \times 0.95C (from the first lot) and 1.5y×0.95C1.5y \times 0.95C (from the second lot): TSP for B=(y+1.5y)×0.95C=2.5y×0.95C=2.375yC\text{TSP for B} = (y + 1.5y) \times 0.95C = 2.5y \times 0.95C = 2.375yC
      • Selling price for type A is x×SA+x×SA=2xSAx \times S_A + x \times S_A = 2xS_A.
    • Therefore, the total selling price is: TSP=2xSA+2.375yC\text{TSP} = 2xS_A + 2.375yC

  5. 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