An article currently costs Rs. 50. If the rate of inflation is 300% per year (that is, the price becomes four times every year), what will be the cost of this article after 2 years, assuming the same rate of inflation continues?

Introduction / Context:
This question uses the idea of compound growth to model inflation. A rate of 300% per year does not mean adding three times the amount; it means the price increases by 300% of its current value, making the new price four times the old price each year. We must find the price after two such yearly increases.

Given Data / Assumptions:

Current cost of the article = Rs. 50.
Inflation rate = 300% per year.
Effective yearly multiplication factor = 1 + 300% = 4.
Time period = 2 years.
Inflation is assumed to compound annually at the same rate.

Concept / Approach:
When values grow at a fixed percentage rate, they follow the compound interest pattern: Future value = Present value * (1 + rate)^time Here rate is 300% per year, so the factor is 4 per year. Over 2 years, we multiply by 4 twice, or more compactly by 4^2.

Step-by-Step Solution:
Step 1: Determine the yearly factor. 1 + 300% = 1 + 3.00 = 4. So each year the price becomes 4 times the previous price. Step 2: Apply the factor for 2 years. After 1 year: Price = 50 * 4 = Rs. 200. After 2 years: Price = 200 * 4 = Rs. 800. Equivalently, price after 2 years = 50 * 4^2 = 50 * 16 = Rs. 800.

Verification / Alternative check:
You can check reasonableness. A 100% increase would double the price each year. A 300% increase is even steeper, so after 2 years the price must be far more than 50 * 2^2 = 200. Our result of 800 fits this expectation and matches the calculation exactly.

Why Other Options Are Wrong:
Rs. 200 is only the price after 1 year, not 2 years. Rs. 600 and Rs. 1000 do not correspond to any correct application of a 4 times yearly factor for an initial value of 50. Only Rs. 800 is consistent with compounding at 300% per year for 2 years.

Common Pitfalls:
Some students confuse 300% with a factor of 3 instead of 4, giving 50 * 3^2 = 450. Others treat 300% as a simple rise of Rs. 150 per year, which ignores compounding and leads to 50 + 150 * 2 = 350. Always convert percentage growth into a multiplicative factor and apply it repeatedly for each time period.

Final Answer:
The cost of the article after 2 years will be Rs. 800.