Every year before the festive season, a brand store increases the price of a product by 42 percent and then offers two successive discounts of 10 percent and 11 percent, respectively. What is the overall percentage gain or loss for the store on that product compared to its original cost price?

Introduction / Context:
This question examines the combined effect of a price hike followed by successive discounts. It is a classic example of successive percentage changes where the order of operations matters. The aim is to see whether these changes result in an overall profit or loss compared to the original cost price.

Given Data / Assumptions:

• Original cost price of the product = C.
• Before the festive season, the price is increased by 42 percent.
• Two successive discounts are then given: first 10 percent, then 11 percent.
• We must compute the net percentage gain or loss relative to the original cost price.

Concept / Approach:
Successive percentage changes are handled by multiplying factors rather than adding or subtracting percentages directly. First we increase the cost by 42 percent to get a new marked price. Then we apply a 10 percent discount on this increased price, followed by an 11 percent discount on the already reduced price. The final selling price is compared to the original cost price to determine net gain or loss percentage.

Step-by-Step Solution:
Assume cost price C = 100 units for convenience. After 42 percent increase, marked price MP = 100 * 1.42 = 142 units. First discount of 10 percent: selling price after first discount = 142 * 0.90 = 127.8 units. Second discount of 11 percent on this new price: final selling price SP = 127.8 * 0.89. Calculate SP = 127.8 * 0.89 = 113.742 units. Net change compared with cost price 100 = 113.742 - 100 = 13.742 units. Percentage gain = 13.742 / 100 * 100 = 13.742 percent gain.

Verification / Alternative check:
We can also express the entire sequence as a single multiplicative factor on cost price. Overall factor = 1.42 (increase) * 0.90 (first discount) * 0.89 (second discount). That product is 1.42 * 0.90 * 0.89 = 1.13742 approximately, which means the final selling price is 1.13742 times the original cost. Therefore the net gain is about 13.742 percent, the same as obtained by direct calculation.

Why Other Options Are Wrong:
3.25% loss or 13.742% loss: These assume the final price fell below cost, which is incorrect because the overall multiplicative factor is greater than 1. 3.25% gain: This underestimates the effect of the initial 42 percent price increase. Only a 13.742 percent gain matches the precise net effect of all the changes.

Common Pitfalls:
A frequent error is to subtract discounts directly from the 42 percent increase, such as 42 - 10 - 11, which ignores the multiplicative nature of successive percentage changes. Another mistake is to apply both discounts directly to the original cost rather than to the updated selling price after each step. Always convert each percentage change into a factor and multiply them in the correct order.

Final Answer:
The store makes an overall gain of approximately 13.742% on the product.