The marked price of a helmet is 30% more than its cost price. If the helmet is sold for Rs 744 after allowing a discount of Rs 36 on the marked price, what is the profit percentage?

Introduction / Context:
This question ties together the relation between cost price, marked price, discount and profit. The marked price is given in relation to cost price, and the final selling price is given after a flat discount. From this, we must backtrack to find the cost price and then compute the profit percentage. This reflects real shop scenarios where products are marked up and then discounted to attract customers while preserving profit.

Given Data / Assumptions:

• Marked price is 30% above cost price.
• Discount given on the marked price is Rs 36.
• Final selling price after discount is Rs 744.
• We need to find the profit percentage.

Concept / Approach:
Let cost price be CP and marked price be MP. We are told MP = CP * 1.30. The selling price is MP minus a fixed discount of Rs 36, and this equals Rs 744. From that, MP can be obtained as 744 + 36. Once MP is known, we find CP using MP = 1.30 * CP. With CP and final SP known, profit percentage formula (SP - CP) / CP * 100 gives the answer.

Step-by-Step Solution:
Let CP be the cost price and MP the marked price of the helmet.MP is 30% above CP, so MP = 1.30 * CP.The helmet is sold for Rs 744 after a discount of Rs 36 on MP.Therefore selling price SP = MP - 36 = Rs 744, so MP = 744 + 36 = Rs 780.Now 780 = 1.30 * CP, so CP = 780 / 1.30 = Rs 600.Profit amount = SP - CP = 744 - 600 = Rs 144.Profit percentage = (144 / 600) * 100 = 24%.

Verification / Alternative check:
We can verify by reversing the steps. Take CP = Rs 600. Marked price at 30% above CP is 600 * 1.30 = Rs 780. Apply a flat discount of Rs 36 to get SP = 780 - 36 = Rs 744. Compare SP with CP: profit is Rs 144 on Rs 600, which is 24%. Everything is consistent with the given conditions.

Why Other Options Are Wrong:
A profit of 18%, 21% or 27% would require different relationships between CP, MP and SP. For example, 18% profit would give SP = 600 * 1.18 = Rs 708, not Rs 744. Hence these options do not match the numerical connection among cost, margin and discount described in the question. Only 24% is correct.

Common Pitfalls:
Some students mistakenly discount from cost price instead of marked price, which changes the arithmetic completely. Others may misinterpret 30% above cost price as 30% of the final selling price. Keeping track of which value each percentage relates to (CP or MP) is crucial to solving such problems correctly.

Final Answer:
The profit percentage on selling the helmet is 24%.