Cost Price Calculation for Shopkeeper Profit

The cost price (CP) is the initial amount the shopkeeper paid for the item. In this problem, the cost price is given as ₹7825.

Marked Price Determination

The shopkeeper marked the item at 30% higher than the cost price. This price is known as the marked price (MP). To calculate the marked price, we increase the cost price by 30%.

The formula is:

$ \text{MP} = \text{CP} \times \left(1 + \frac{\text{Markup Percentage}}{100}\right) $

Given CP = ₹7825 and Markup Percentage = 30%:

$ \text{MP} = 7825 \times \left(1 + \frac{30}{100}\right) $

$ \text{MP} = 7825 \times (1 + 0.30) $

$ \text{MP} = 7825 \times 1.30 $

$ \text{MP} = 10172.50 $

So, the marked price is ₹10172.50.

Selling Price After Discount

The shopkeeper offers a 20% discount on the marked price. This discount reduces the price the customer pays, which is the selling price (SP). The discount is calculated on the marked price.

The discount amount is calculated as:

$ \text{Discount Amount} = \text{MP} \times \frac{\text{Discount Percentage}}{100} $

$ \text{Discount Amount} = 10172.50 \times \frac{20}{100} $

$ \text{Discount Amount} = 10172.50 \times 0.20 = 2034.50 $

The selling price is the marked price minus the discount amount:

$ \text{SP} = \text{MP} - \text{Discount Amount} $

$ \text{SP} = 10172.50 - 2034.50 $

$ \text{SP} = 8138.00 $

Alternatively, using a direct formula:

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

$ \text{SP} = 10172.50 \times \left(1 - \frac{20}{100}\right) $

$ \text{SP} = 10172.50 \times 0.80 $

$ \text{SP} = 8138.00 $

Therefore, the selling price is ₹8138.00.

Profit Calculation and Percentage

Profit is the financial gain when the selling price is more than the cost price. It is calculated as:

$ \text{Profit} = \text{SP} - \text{CP} $

$ \text{Profit} = 8138.00 - 7825.00 $

$ \text{Profit} = 313.00 $

The shopkeeper earned a profit of ₹313.00.

The profit percentage measures this profit relative to the cost price. The formula is:

$ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 $

Substituting the values:

$ \text{Profit Percentage} = \left(\frac{313.00}{7825.00}\right) \times 100 $

$ \text{Profit Percentage} = 0.04 \times 100 $

$ \text{Profit Percentage} = 4\% $

The calculated profit percentage is 4%.