When a discount of 20% is given on a jacket, the profit is 28%. If instead the discount is reduced to 13% on the same marked price, what will be the profit percentage?

Introduction / Context:
This question is very similar to earlier discount and profit problems. It explores how changing the discount on a fixed marked price alters the final profit percentage, given that cost price remains constant. Such questions are standard when learning how selling strategies affect margins in retail scenarios.

Given Data / Assumptions:

• At 20% discount, the seller gets 28% profit.
• At 13% discount, we need to find the new profit percentage.
• The marked price of the jacket is constant in both cases.
• The cost price remains unchanged.

Concept / Approach:
Let CP be cost price and MP be marked price. With a 20% discount, SP1 = MP * 0.80 = CP * 1.28. This equality lets us express MP in terms of CP. Then, with a 13% discount, SP2 = MP * 0.87. Substituting MP from the first relation, we find SP2 in terms of CP and compute profit percentage as (SP2 - CP) / CP * 100.

Step-by-Step Solution:
Let CP be the cost price and MP the marked price of the jacket.With 20% discount, SP1 = MP * (1 - 20 / 100) = 0.80 * MP.Profit here is 28%, so SP1 = CP * 1.28.Thus 0.80 * MP = 1.28 * CP, so MP = (1.28 / 0.80) * CP = 1.6 * CP.With 13% discount, SP2 = MP * (1 - 13 / 100) = 0.87 * MP.Substituting MP, SP2 = 0.87 * 1.6 * CP = 1.392 * CP.Profit percentage now = (SP2 - CP) / CP * 100 = (1.392 * CP - CP) / CP * 100 = 0.392 * 100 = 39.2 percent.

Verification / Alternative check:
Assume CP = Rs 100. Then MP = 1.6 * 100 = Rs 160. With 20% discount, SP1 = 0.80 * 160 = Rs 128, which is exactly 28% profit on Rs 100. With 13% discount, SP2 = 0.87 * 160 = Rs 139.2. Profit = 39.2 on cost 100, i.e., 39.2%. This confirms that our result is consistent.

Why Other Options Are Wrong:
41 percent, 42.8 percent or 37.4 percent all correspond to different selling prices for the same cost price and do not match the actual SP2 derived from the discount formula. Only 39.2 percent exactly matches the change from 20% discount with 28% profit to 13% discount.

Common Pitfalls:
Students may try to simply add 7 percentage points to the profit when the discount is reduced by 7 percentage points, which is not generally valid because discounts work on marked price and profits on cost price. Another common error is to miscalculate the multiplier for profit and discount combinations. Writing each step clearly in terms of CP and MP helps avoid such mistakes.

Final Answer:
With a 13% discount, the profit on the jacket is 39.2 percent.