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The selling price of 15 articles is equal to the cost price of 20 articles. Find the profit percentage.

Mathematics

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Answer

3313% profit33\frac{1}{3}\% \text{ profit}

Step-by-step solution

5 steps

  1. Understand the given relationship between selling price (SP) and cost price (CP).

    The question states that the selling price of 15 articles is equal to the cost price of 20 articles.
    Let SPSP be the selling price of one article and CPCP be the cost price of one article.
    According to the problem:

    15×SP=20×CP15 \times SP = 20 \times CP

  2. Find the ratio of SPSP to CPCP.

    Divide both sides by 15×CP15 \times CP:

    SPCP=2015\frac{SP}{CP} = \frac{20}{15}

    Simplify the fraction:

    SPCP=43\frac{SP}{CP} = \frac{4}{3}

    This implies that SP=43CPSP = \frac{4}{3} CP.

  3. Determine if there is a profit or loss.

    Since SP=43CPSP = \frac{4}{3} CP, and 43>1\frac{4}{3} > 1, it means SP>CPSP > CP. Therefore, there is a profit.

  4. Calculate the profit.

    Profit = SP−CPSP - CP
    Substitute the expression for SPSP:

    Profit=43CP−CPProfit = \frac{4}{3} CP - CP Profit=(43−1)CPProfit = \left(\frac{4}{3} - 1\right) CP Profit=(4−33)CPProfit = \left(\frac{4-3}{3}\right) CP Profit=13CPProfit = \frac{1}{3} CP

  5. Calculate the profit percentage.

    The formula for profit percentage is:

    Profit Percentage=ProfitCP×100%Profit \text{ Percentage} = \frac{Profit}{CP} \times 100\%

    Substitute the calculated profit:

    Profit Percentage=13CPCP×100%Profit \text{ Percentage} = \frac{\frac{1}{3} CP}{CP} \times 100\% Profit Percentage=13×100%Profit \text{ Percentage} = \frac{1}{3} \times 100\% Profit Percentage=1003%Profit \text{ Percentage} = \frac{100}{3}\% Profit Percentage=3313%Profit \text{ Percentage} = 33\frac{1}{3}\%

    The overall profit percentage is 3313%33\frac{1}{3}\%.

    The final answer is 3313% profit33\frac{1}{3}\% \text{ profit}.

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