
Shortcut Trick
If the Cost Price (CP) and Selling Price (SP) are both increased or decreased by the same percentage, the Profit Percentage remains unchanged.
Initial Profit = 10% ⇒ Ratio CP : SP = 100 : 110 = 10 : 11.
Both values are decreased by 20%, which means they are multiplied by a factor of 0.8.
New Ratio = (10 × 0.8) : (11 × 0.8) = 8 : 8.8 = 10 : 11.
Since the ratio remains 10 : 11, the profit percentage remains 10%.
∴ The correct answer is 10%.

Alternate Method
Given:
Initial profit percentage = 10%
Reduction in Cost Price (CP) = 20%
Reduction in Selling Price (SP) = 20%
Formula Used:
SP = CP × (100 + Profit%) ÷ 100
Profit% = [(SP − CP) ÷ CP] × 100

⇒ Let the Initial Cost Price (CP1) = 100 ⇒ Since Profit is 10%, Initial Selling Price (SP1) = 100 + 10 = 110 ⇒ New Cost Price (CP2) = 100 − 20% of 100 = 100 − 20 = 80 ⇒ New Selling Price (SP2) = 110 − 20% of 110 = 110 − 22 = 88 ⇒ New Profit = SP2 − CP2 = 88 − 80 = 8 ⇒ New Profit Percentage = (New Profit ÷ New CP) × 100 ⇒ New Profit % = (8 ÷ 80) × 100 = (1 ÷ 10) × 100 = 10%
∴ The correct answer is 10%.

Additional Information
Effect of Scaling on Percentages
If all terms in a ratio (like CP and SP) are multiplied or divided by the same non-zero constant, the ratio remains equivalent, and the resulting percentage (Profit or Loss) remains unchanged.
Marked Price and Discount
Selling Price can also be calculated as Marked Price (MP) × (100 − Discount%) ÷ 100. Profit is always calculated on CP, while Discount is calculated on MP.
Net Profit after Successive Changes
If CP changes by x% and SP changes by y%, the new profit percentage must be found by calculating the new absolute values of CP and SP individually.