Lucky started working two years ago. At that time her starting salary was exactly half of Karthik salary. Since then, both Lucky and Karthik have received a yearly salary increase of 10% each. What percentage of Karthik current salary is equal to Lucky current salary (rounded to the nearest percent)?

Introduction / Context:
This question combines percentage growth with ratio comparison. Both employees receive the same percentage raise each year, but their starting salaries are different. The problem asks you to compare their current salaries after two years of 10% annual increments. Understanding how equal percentage changes affect ratios is essential for solving many salary, population, and investment problems.

Given Data / Assumptions:

Let Karthik starting salary be K rupees.

Lucky starting salary is half of that, that is K / 2 rupees.

Both Lucky and Karthik receive a 10% salary increase every year.

We are dealing with a period of two years.

We need the ratio Lucky current salary ÷ Karthik current salary expressed as a percentage.

Concept / Approach:
If two quantities are increased or decreased by the same percentage, their ratio remains unchanged. Here both Lucky and Karthik receive 10% raises in each of the two years, so their salaries are each multiplied by the same factor (1.1 twice). Therefore, even after the raises, Lucky salary will remain exactly half of Karthik salary. After recognizing this, we simply convert the ratio to a percentage.

Step-by-Step Solution:
Step 1: Let Karthik initial salary be K.Step 2: Lucky initial salary = K / 2.Step 3: After one year, both salaries are multiplied by 1.1 (since 10% increase means multiply by 1.10).After two years, each salary is multiplied by (1.1)^2 = 1.21.Step 4: Karthik current salary = K * 1.21.Step 5: Lucky current salary = (K / 2) * 1.21 = 0.5 * K * 1.21.Step 6: Ratio Lucky current salary to Karthik current salary = (0.5 * K * 1.21) / (K * 1.21) = 0.5.Step 7: Convert 0.5 to a percentage: 0.5 * 100 = 50%.

Verification / Alternative check:
You can test with actual numbers. Suppose Karthik started at Rs. 20,000 and Lucky at Rs. 10,000. After two years, both get 10% raises each year. Karthik salary becomes 20,000 * 1.21 = 24,200. Lucky salary becomes 10,000 * 1.21 = 12,100. Now 12,100 is exactly half of 24,200, confirming the 50% ratio.

Why Other Options Are Wrong:
75%, 35%, and 60% assume that equal percentage increases can change the original half relationship, which is not correct.
22.5% is far too small and does not relate to the original ratio of 1 : 2.

Common Pitfalls:
Many candidates try to compute each salary year by year using absolute amounts and then divide, which is fine but more time consuming. Others mistakenly think that because both salaries grow at the same rate, their difference remains constant while the ratio changes. In percentage growth problems, remember that equal percentage changes preserve the original ratio even though the absolute difference between the two salaries may increase.

Final Answer:
Lucky current salary is 50% of Karthik current salary.