A 35% profit is made when a discount of 35% is given on the marked price of an item. When the discount is 45%, then the profit percentage will be:

Given:

A 35% profit is made when a discount of 35% is given on the marked price of an item.

Formula used:

Let MP be the marked price, CP be the cost price, and SP be the selling price.

SP = MP × (1 - Discount%)

Profit% = [(SP - CP) / CP] × 100

Calculations:

Given, Profit% = 35% and Discount% = 35%

⇒ SP = MP × (1 - 0.35)

⇒ SP = MP × 0.65

Profit% = [(MP × 0.65 - CP) / CP] × 100 = 35%

⇒ (MP × 0.65 - CP) / CP = 0.35

⇒ MP × 0.65 - CP = 0.35 CP

⇒ MP × 0.65 = 1.35 CP

⇒ MP = 1.35 CP / 0.65

For a 45% discount:

⇒ SP = MP × (1 - 0.45)

⇒ SP = MP × 0.55

⇒ Profit% = [(SP - CP) / CP] × 100

⇒ Profit% = [(MP × 0.55 - CP) / CP] × 100

⇒ Profit% = [(1.35 CP / 0.65 × 0.55 - CP) / CP] × 100

⇒ Profit% = [(1.35 × 0.55 / 0.65 - 1) / 1] × 100

⇒ Profit% = [(0.7425 / 0.65 - 1) / 1] × 100

⇒ Profit% = [1.1423 - 1] × 100

⇒ Profit% = 0.1423 × 100

⇒ Profit% = \(14\frac{3}{13}\)%

∴ The correct answer is \(14\frac{3}{13}\)%.