Calculating Marked Price with Discount and Profit Percentage

This problem involves understanding the relationship between Cost Price (CP), Selling Price (SP), Marked Price (MP), discount percentage, and profit percentage. The shopkeeper buys an article, marks up its price, offers a discount on the marked price to sell it, and still makes a profit on the original cost price.

Key Concepts in Pricing

• Cost Price (CP): The price at which the shopkeeper buys the article. In this case, it's Rs. 600.
• Marked Price (MP): The price printed on the article or the price the shopkeeper initially sets. The discount is calculated on this price. We need to find this.
• Selling Price (SP): The price at which the shopkeeper sells the article to the customer. This is arrived at after giving a discount on the MP. This is also the price at which the profit is calculated relative to the CP.
• Discount: A reduction offered on the Marked Price. Given as 20%.
• Profit: The difference between the Selling Price and the Cost Price when SP > CP. Calculated as a percentage of the Cost Price. Given as 25%.

Step-by-Step Solution

Step 1: Calculate the Selling Price (SP)

We know the Cost Price (CP) and the Profit Percentage. The Selling Price can be calculated using the formula:

$\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right)$

Given:

• CP = Rs. 600
• Profit % = 25%

Let's plug in the values:

$\text{SP} = 600 \times \left(1 + \frac{25}{100}\right)$

$\text{SP} = 600 \times \left(1 + 0.25\right)$

$\text{SP} = 600 \times 1.25$

$\text{SP} = 750$

So, the Selling Price of the article is Rs. 750.

Step 2: Calculate the Marked Price (MP)

We know the Selling Price (SP) and the Discount Percentage. The Selling Price is obtained after giving a discount on the Marked Price. The relationship is given by the formula:

$\text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount \%}}{100}\right)$

Given:

• SP = Rs. 750 (Calculated in Step 1)
• Discount % = 20%

Let's plug in the values and solve for MP:

$750 = \text{MP} \times \left(1 - \frac{20}{100}\right)$

$750 = \text{MP} \times \left(1 - 0.20\right)$

$750 = \text{MP} \times 0.80$

To find MP, we rearrange the formula:

$\text{MP} = \frac{750}{0.80}$

To make the division easier, we can write 0.80 as 4/5 or multiply both numerator and denominator by 100:

$\text{MP} = \frac{750 \times 100}{0.80 \times 100} = \frac{75000}{80}$

Now, perform the division:

$\text{MP} = \frac{7500}{8}$

$\text{MP} = 937.50$

Thus, the Marked Price of the article is Rs. 937.50.

Summary of Calculations

The Marked Price of the article which costs Rs. 600 to the shopkeeper, allowing a 20% discount and still gaining 25%, is Rs. 937.50.

Revision Table: Profit, Loss, and Discount

Additional Information on Shopkeeper Calculations

Shopkeepers use these percentage concepts to set prices strategically. They first decide on the desired profit margin based on the cost price. This determines the selling price. Knowing the selling price, they then calculate what marked price they need to set so that after offering a standard discount (which attracts customers), the price reduces exactly to the calculated selling price.

The relationship between CP, MP, Profit %, and Discount % can also be expressed using a single formula:

$\text{MP} = \text{CP} \times \frac{100 + \text{Profit \%}}{100 - \text{Discount \%}}$

Let's verify this using our values:

CP = 600, Profit % = 25, Discount % = 20

$\text{MP} = 600 \times \frac{100 + 25}{100 - 20}$

$\text{MP} = 600 \times \frac{125}{80}$

$\text{MP} = 600 \times \frac{125}{80} = 600 \times \frac{25}{16}$ (Dividing numerator and denominator by 5)

$\text{MP} = \frac{600 \times 25}{16} = \frac{15000}{16}$

$\text{MP} = \frac{7500}{8} = 937.50$

This formula provides a quicker way to find the Marked Price directly from the Cost Price, Profit Percentage, and Discount Percentage, bypassing the intermediate calculation of Selling Price.