When a discount of 25% is given on a wedding gown, the seller still makes a profit of 32%. If instead the discount is reduced to 17% on the same marked price, what will be the new profit percentage?

Introduction / Context:
This problem again explores the connection between discount and profit on the same item. The wedding gown has a fixed marked price, but changing the discount changes the selling price and therefore the profit percentage. The question checks how well you can move between marked price, cost price and selling price when two different discount situations are given.

Given Data / Assumptions:

• Discount of 25% on the marked price gives a profit of 32%.
• Discount of 17% on the same marked price is considered next.
• We need to find the profit percentage in the second case.
• The cost price and marked price of the gown remain the same in both scenarios.

Concept / Approach:
Let MP be the marked price and CP be the cost price. When discount is 25%, the selling price is MP * 0.75 and this equals CP * 1.32. From this relation we can express MP in terms of CP. Then for a discount of 17%, the selling price is MP * 0.83. Using the MP obtained earlier, we compute the new selling price and then the new profit percentage by comparing it to CP.

Step-by-Step Solution:
Let cost price be CP and marked price be MP.With 25% discount, selling price SP1 = MP * (1 - 25 / 100) = 0.75 * MP.Given profit here is 32%, so SP1 = CP * 1.32.Thus 0.75 * MP = 1.32 * CP, so MP = (1.32 / 0.75) * CP = 1.76 * CP.With 17% discount, selling price SP2 = MP * (1 - 17 / 100) = 0.83 * MP.Using MP = 1.76 * CP, SP2 = 0.83 * 1.76 * CP = 1.4608 * CP.Profit percentage in this case = (SP2 - CP) / CP * 100 = (1.4608 * CP - CP) / CP * 100 = 0.4608 * 100 = 46.08%.

Verification / Alternative check:
Take CP = Rs 100 as a simple assumption. Then MP = 1.76 * 100 = Rs 176. With 25% discount, SP1 = 0.75 * 176 = Rs 132, which is exactly a 32% profit on Rs 100. With 17% discount, SP2 = 0.83 * 176 = Rs 146.608, whose profit on Rs 100 is 46.08%. This numerical check supports our algebraic work.

Why Other Options Are Wrong:
Values like 43.16%, 49% or 51.03% correspond to different discount or cost price relationships and are not consistent with the derived marked price. Only 46.08% matches the exact profit percentage obtained from the correct formula and the given conditions.

Common Pitfalls:
One common mistake is to think that a decrease in discount of 8 percentage points always increases profit by exactly 8 percentage points. This is not true because discount works on marked price and profit works on cost price. The correct approach is always to move stepwise through MP and CP with precise multipliers.

Final Answer:
With a 17% discount, the new profit percentage will be 46.08%.