When a discount of 20% is given on a movie ticket, the seller makes a profit of 34%. If instead the discount is 15%, what will be the new percentage profit?

Introduction / Context:
This question is another example involving marked price, discount, and profit. Initially a 20% discount produces a profit of 34%. The discount is then reduced to 15%, and we must determine the new profit percentage given that the cost price does not change. Such problems appear frequently in profit and loss sections of aptitude tests.

Given Data / Assumptions:

• Marked price (MP) of the movie ticket is some value M.
• With 20% discount, profit is 34%.
• With 15% discount, cost price remains the same.
• We must compute new profit percentage with a 15% discount.

Concept / Approach:
First scenario: SP1 = 0.80M (due to 20% discount). This SP1 corresponds to a 34% profit on cost price: SP1 = 1.34 * CP, so CP = SP1 / 1.34 = 0.80M / 1.34. Second scenario: SP2 = 0.85M (due to 15% discount). Using the same CP, profit percentage with SP2 is (SP2 - CP) / CP * 100. Substituting CP in terms of M gives the exact new profit percentage.

Step-by-Step Solution:
Let MP = M. With 20% discount, SP1 = 0.80M. Given profit = 34%, so SP1 = 1.34 * CP → CP = 0.80M / 1.34. With 15% discount, SP2 = 0.85M. New profit percentage = [(SP2 - CP) / CP] * 100. Substitute CP: Profit% = [(0.85M - 0.80M/1.34) / (0.80M/1.34)] * 100. Simplify the expression to obtain profit% ≈ 42.375%.

Verification / Alternative check:
Choose M = Rs 134 for convenience. Then SP1 = 0.80 * 134 = Rs 107.2. Given SP1 is 34% above CP, CP = 107.2 / 1.34 = Rs 80. With 15% discount, SP2 = 0.85 * 134 = Rs 113.9. Profit = 113.9 - 80 = Rs 33.9 and profit percentage = (33.9 / 80) * 100 ≈ 42.375%, confirming the result.

Why Other Options Are Wrong:
49% and 55.625% are significantly higher than the calculated value and would correspond to very small cost prices. A profit of 35.75% is only slightly above 34% and does not match the precise calculation. Only 42.375% is consistent with the algebraic and numerical computations.

Common Pitfalls:
A common mistake is to subtract or add discount percentages directly without recomputing selling price. Another is to assume profit percentage changes linearly with discount. Some students also confuse profit on marked price with profit on cost price, leading to wrong equations.

Final Answer:
With a 15% discount, the new profit percentage becomes approximately 42.375 percent.