A salesman calculates his profit on the marked (list) price and finds it to be 30%. He forgets that he actually gave a discount of 20% to the customer. What is his actual profit percentage on the cost price?

Introduction / Context:
This question explores the difference between profit calculated on marked price and the actual profit when a discount is given. The salesman incorrectly computes his profit as 30% of the marked price, ignoring the 20% discount he has granted. We must determine the true profit percentage on the cost price. This involves understanding the relationships between marked price, cost price, discount and actual selling price.

Given Data / Assumptions:

• Let marked price be M rupees.
• The salesman thinks his profit is 30% of the marked price.
• Thus, he assumes (M - cost price) / M = 30%.
• He actually gives a discount of 20%, so the real selling price is 80% of M.
• We need the actual profit percentage based on cost price.

Concept / Approach:
The salesman says his profit on the marked price is 30%, which we interpret as (M - CP) / M = 0.30, where CP is cost price. From this we can find CP in terms of M. The real selling price must be SP = 0.80M, because of the 20% discount. Then actual profit on cost price is (SP - CP) / CP * 100. The key step is to correctly understand that his 30% is calculated on M, not on CP, and that he forgets the discount when making this calculation.

Step-by-Step Solution:
Step 1: Let marked price = M and cost price = CP. Step 2: Salesman calculates profit on M, so (M - CP) / M = 30/100 = 0.30. Step 3: Therefore, M - CP = 0.30M. Step 4: Rearranging: CP = M - 0.30M = 0.70M. Step 5: He actually gives 20% discount, so true selling price SP = 0.80M. Step 6: Actual profit = SP - CP = 0.80M - 0.70M = 0.10M. Step 7: Actual profit percentage on CP = (0.10M / 0.70M) * 100. Step 8: Simplify fraction: 0.10M / 0.70M = (1/10) / (7/10) = 1/7. Step 9: Profit percentage = (1/7) * 100 = 100/7% ≈ 14.2857%.

Verification / Alternative check:
Choose a convenient marked price, say M = Rs. 700. From CP = 0.70M, we get CP = Rs. 490. According to his mistaken calculation, he thinks profit is M - CP = 700 - 490 = Rs. 210, which is 30% of 700. In reality, he sells at a 20% discount: SP = 0.80 * 700 = Rs. 560. Actual profit is 560 - 490 = Rs. 70. Profit percentage on CP = (70 / 490) * 100 = (1/7) * 100 = 100/7%, confirming our result.

Why Other Options Are Wrong:
A profit of 60% would require SP = 1.6CP, far above 0.80M, while 22.5%, 18.4% or 260/11% (which is about 23.64%) do not match the exact fraction 1/7 arising from the proper equations. Only 100/7% aligns with both the given mistaken calculation and the actual discount applied.

Common Pitfalls:
Many candidates misinterpret the phrase "profit on the marked price" and accidentally compute (SP - CP) / CP = 30% or equate profit directly to 30% of cost price. Others forget to apply the discount to the marked price when determining the actual selling price. Carefully distinguishing which base the percentage refers to, and systematically expressing all values in terms of M, prevents these mistakes.

Final Answer:
The salesman's actual profit percentage is 100/7%, which is approximately 14.29%.