Net effect of increase and successive discounts: If the price of an item is first increased by 30% and then two successive discounts of 10% and 10% are allowed, what is the overall price change?

Introduction / Context:
This question examines multiplicative chaining of one increase and two successive discounts. We track the net factor relative to the original price to see the overall effect as an increase or decrease and by how much percent.

Given Data / Assumptions:
Start price = P. Apply +30%, then two discounts of 10% each.

Concept / Approach:
Net factor = 1.30 * 0.90 * 0.90 = 1.30 * 0.81 = 1.053. This factor shows the final price as a proportion of the original P, i.e., a 5.3% increase.

Step-by-Step Solution:

Verification / Alternative check:
Use P = 100; sequence gives 100 → 130 → 117 → 105.3.

Why Other Options Are Wrong:
10% increase ignores the compounding; 3% or −5.3% have wrong signs; “No change” is incorrect.

Common Pitfalls:
Adding and subtracting percentages linearly; always multiply the factors.

Final Answer:
Increased by 5.3%