Profit or Loss Percent Calculation

Let the Cost Price (CP) be $100$. This assumption simplifies percentage calculations.

Marked Price Calculation

The shopkeeper adds 20% on the cost price to set the marked price.

MP = CP + (20\% \times \text{CP})

MP = 100 + (\frac{20}{100} \times 100)

MP = 100 + 20 = 120

Selling Price Calculation

A discount of 20% is given on the marked price.

Discount Amount = 20\% \times \text{MP}

Discount Amount = \frac{20}{100} \times 120 = 24

SP = MP - \text{Discount Amount}

SP = 120 - 24 = 96

Profit or Loss Check

Compare the Selling Price (SP) with the Cost Price (CP).

• CP = $100
• SP = $96

Since SP < CP, there is a loss.

Loss Percent Calculation

Loss = CP - SP

Loss = 100 - 96 = 4

Loss Percent = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100

Loss Percent = \left( \frac{4}{100} \right) \times 100 = 4\%

Therefore, the shopkeeper incurred a 4% loss.