Every year before the festive season, a shopkeeper increases the price of a product by 35% and then offers two successive discounts of 10% and 15%; what is the net percentage profit or loss on the original price?

Introduction / Context:
This question examines combined percentage changes involving a price increase followed by two successive discounts. Such situations are common in sales and marketing strategies where a marked up price is later shown as discounted. The task is to determine whether the shopkeeper finally makes a profit or a loss with respect to the original price, and by what percentage.

Given Data / Assumptions:

• Original price of the product is assumed to be some base amount, say Rs. 100.
• Price is first increased by 35% before the festival.
• Two successive discounts are then applied: first 10%, then 15% on the reduced price.
• No additional taxes or costs are considered.
• We need to find the net percentage profit or loss relative to the original price.

Concept / Approach:
Percentage increase and successive discounts are multiplicative factors on the original price. A 35% increase multiplies the price by 1.35. A 10% discount multiplies by 0.90 and a further 15% discount multiplies by 0.85. The final price factor is therefore original price multiplied by 1.35 * 0.90 * 0.85. Comparing this final price with the original price indicates whether there is a net gain or loss and by what percentage. This approach avoids handling actual rupee values and works entirely with percentage multipliers.

Step-by-Step Solution:
Step 1: Let the original price of the product be Rs. 100.Step 2: Price is increased by 35%, so new price after increase = 100 * 1.35 = Rs. 135.Step 3: First discount of 10% is applied on Rs. 135.Step 4: Price after first discount = 135 * 0.90 = Rs. 121.50.Step 5: Second discount of 15% is then applied on Rs. 121.50.Step 6: Price after second discount = 121.50 * 0.85.Step 7: Compute 121.50 * 0.85 = 103.275, so final selling price ≈ Rs. 103.28.Step 8: Compare final price with original price Rs. 100.Step 9: Net change = 103.275 - 100 = Rs. 3.275 profit.Step 10: Profit percentage = (3.275 / 100) * 100 = 3.275% ≈ 3.27% gain.

Verification / Alternative check:
Using the multiplicative factor method, the overall multiplier from original price to final price is 1.35 * 0.90 * 0.85. Compute this: 1.35 * 0.90 = 1.215. Now 1.215 * 0.85 = 1.03275. This means final price is 1.03275 times the original, or 103.275% of the original. Therefore net gain percentage = 103.275 - 100 = 3.275% gain. This matches the stepwise money calculation and confirms that the result is approximately 3.27% gain.

Why Other Options Are Wrong:

• 3.27% loss: This would require final price to be 96.73% of the original, which is not the case here.
• 4.15% loss or 4.15% gain: These values do not match the accurate combined percentage multiplier 1.03275 and are simply distractor options.

Common Pitfalls:

• Adding percentages linearly, for example 35% minus 10% minus 15% and concluding a 10% rise, which ignores the multiplicative nature of successive changes.
• Applying both discounts on the original price instead of sequentially, which changes the final price.
• Incorrect decimal multiplication or rounding too aggressively, which may slightly distort the final percentage.

Final Answer:
The shopkeeper makes a net 3.27% gain on the original price after increasing the price and then giving the two successive discounts.