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Calculate the Selling Price (SP) based on the Cost Price (CP) and profit percentage.

Business/Management

ScanSolve AI Answer

Answer

40%\text{40\%}

Step-by-step solution

5 steps
  1. Calculate the Selling Price (SP) based on the Cost Price (CP) and profit percentage.

    The shopkeeper gains 33% profit.

    SP=CP+0.33×CP=1.33×CP\text{SP} = \text{CP} + 0.33 \times \text{CP} = 1.33 \times \text{CP}
  2. Calculate the Selling Price (SP) based on the Marked Price (MP) and discount percentage.

    The shopkeeper gives a 5% discount on the Marked Price.

    SP=MP−0.05×MP=0.95×MP\text{SP} = \text{MP} - 0.05 \times \text{MP} = 0.95 \times \text{MP}
  3. Equate the two expressions for Selling Price (SP) to find the relationship between Marked Price (MP) and Cost Price (CP).

    1.33×CP=0.95×MP1.33 \times \text{CP} = 0.95 \times \text{MP}
  4. Solve for Marked Price (MP) in terms of Cost Price (CP).

    MP=1.330.95×CP\text{MP} = \frac{1.33}{0.95} \times \text{CP} MP=13395×CP\text{MP} = \frac{133}{95} \times \text{CP} MP=1.4×CP\text{MP} = 1.4 \times \text{CP}
  5. Calculate the percentage above the Cost Price that the article must be marked.

    The percentage above CP is given by MP−CPCP×100%\frac{\text{MP} - \text{CP}}{\text{CP}} \times 100\%.

    Percentage above CP=1.4×CP−CPCP×100%\text{Percentage above CP} = \frac{1.4 \times \text{CP} - \text{CP}}{\text{CP}} \times 100\% Percentage above CP=0.4×CPCP×100%\text{Percentage above CP} = \frac{0.4 \times \text{CP}}{\text{CP}} \times 100\% Percentage above CP=0.4×100%\text{Percentage above CP} = 0.4 \times 100\% Percentage above CP=40%\text{Percentage above CP} = 40\%

    The article must be marked 40% above the Cost Price.

    The correct option is 2.
    The final answer is \text{40%}.

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