Kanchan bought a clock at 25% discount on its marked price and later sold it at a 75% gain on the price she paid. What was her profit percentage calculated on the original marked price of the clock?

Introduction / Context:
This question belongs to the topic of profit, loss, and discount in arithmetic. Kanchan buys a clock at a discount on the marked price (label price) and then sells it at a profit based on her purchase price. The key is to compute her final selling price relative to the original marked price and then express the gain as a percentage of the marked price, not of her cost price. Such questions are very common in competitive exams and require clear understanding of successive percentage changes.

Given Data / Assumptions:

• Let the marked price (MP) of the clock be taken as Rs. 100 for convenience.

• Discount given on the marked price = 25%.

• Kanchan buys the clock after discount and later sells it at a 75% gain on her cost price.

• We must find profit percentage with respect to the original marked price.

Concept / Approach:
To solve such problems easily, we assume a convenient marked price, typically Rs. 100. After applying the discount, we get Kanchan's cost price. Then, using the given percentage gain, we compute her selling price. Finally, we compare this selling price with the original marked price to obtain the required profit percentage on the marked price. Using a convenient assumed value simplifies percentage calculations without affecting the final percentage result.

Step-by-Step Solution:
Step 1: Assume the marked price (MP) = Rs. 100. Step 2: A discount of 25% on the marked price means Kanchan pays 75% of the MP. Step 3: Cost price (CP) for Kanchan = 75% of 100 = Rs. 75. Step 4: She sells the clock at a 75% gain on her cost price. Step 5: Selling price (SP) = CP * (1 + 75/100) = 75 * 1.75. Step 6: 75 * 1.75 = 75 * (7/4) = (75 * 7) / 4 = 525 / 4 = Rs. 131.25. Step 7: Profit calculated on the marked price = SP − MP = 131.25 − 100 = Rs. 31.25. Step 8: Profit percentage on the marked price = (31.25 / 100) * 100% = 31.25%.

Verification / Alternative check:
We can also compute directly as a combined effect: effective value of SP as a percentage of MP = (remaining after discount) * (multiplier for profit) = 75% of MP * 175% (1.75) of CP. So SP as % of MP = 0.75 * 1.75 * 100% = 1.3125 * 100% = 131.25% of MP. Thus, profit on MP = 131.25% − 100% = 31.25%, which confirms the earlier result.

Why Other Options Are Wrong:
• 50%: This would imply a selling price of 150% of MP, inconsistent with the successive changes (25% discount then 75% gain).
• 56.25%: This might arise from misapplying percentage gain directly to marked price or confusing compounding effects.
• 60%: This is a large overestimate and does not match the exact calculation from cost price to selling price relative to the original MP.

Common Pitfalls:
A frequent mistake is to calculate profit percentage on the cost price and then present that as the profit on the marked price. Another error is to add or subtract percentages directly (for example, thinking 75% gain minus 25% discount equals 50% profit on MP). Successive percentages must be applied multiplicatively, not simply added or subtracted. Using an assumed marked price of Rs. 100 helps keep the logic and arithmetic clear.

Final Answer:
Kanchan's profit percentage calculated on the original marked price of the clock is 31.25%.