When an African safari ticket is sold with a discount of 20% on its marked price, the seller makes a profit of 43%. If instead the discount allowed is 28%, what will be the new percentage profit?

Introduction / Context:
This question links marked price, discount percentage, and profit percentage. It first gives a scenario where a certain discount results in a known profit. Then it changes the discount and asks for the new profit percentage, assuming cost price remains the same. This is a common pattern in retail profit and loss questions.

Given Data / Assumptions:

• Marked price (MP) of the ticket is some value M.
• With a 20% discount, profit is 43%.
• With a 28% discount, cost price (CP) is unchanged and we must find the new profit percentage.
• No extra costs such as taxes are considered.

Concept / Approach:
First, express the selling price after 20% discount in terms of M, then relate it to cost price using the 43% profit. This allows us to find CP in terms of M. Next, compute the selling price with 28% discount and use the same CP to calculate the new profit percentage: Profit% = (SP2 - CP) / CP * 100.

Step-by-Step Solution:
Let the marked price be M. With 20% discount, selling price SP1 = 0.80M. Profit on SP1 is 43%, so SP1 = CP * 1.43 → CP = SP1 / 1.43 = 0.80M / 1.43. With 28% discount, selling price SP2 = 0.72M. Profit percentage with SP2 is: Profit% = [(SP2 - CP) / CP] * 100. Substitute CP: Profit% = [(0.72M - 0.80M/1.43) / (0.80M/1.43)] * 100. Simplify the fraction to obtain profit percentage ≈ 28.7%.

Verification / Alternative check:
Choose a convenient marked price, say M = Rs 143. Then SP1 = 0.80 * 143 = Rs 114.40. Since profit is 43%, CP = 114.40 / 1.43 = Rs 80. With 28% discount, SP2 = 0.72 * 143 = Rs 102.96. Profit = 102.96 - 80 = Rs 22.96. Profit percentage = (22.96 / 80) * 100 ≈ 28.7%. This numerical check confirms the derived result.

Why Other Options Are Wrong:
71% and 113.3% are far higher than 43% and do not match the computation. A profit of 13.6% is too low given that the discount is only slightly higher than before and the initial profit was already 43%. Only 28.7% fits the exact calculations.

Common Pitfalls:
A typical error is to treat profit percentage directly on marked price instead of cost price. Another mistake is to subtract discount percentages or profit percentages directly without recalculating selling price and cost price. Always recompute CP from the first scenario before working out the effect of the new discount.

Final Answer:
With a 28% discount, the new profit percentage is approximately 28.7 percent.