Pranita scores 30 marks more in Mathematics than in Science, and her Mathematics marks are 60 percent of the sum of her Mathematics and Science marks. What are her Science marks?

Introduction / Context:
This question is a classic example of using percentages in combination with a difference between two quantities. It involves forming and solving a simple linear equation by translating the word statement about marks into algebraic relationships. Such problems appear frequently in exam sections about percentages and ratios.

Given Data / Assumptions:
- Let Science marks be S.
- Mathematics marks are 30 more than Science marks, so Mathematics marks = S + 30.
- Mathematics marks are 60 percent of the sum of Mathematics and Science marks.
- So S + 30 = 60 percent of (S + S + 30).
- We must find S, the Science marks.

Concept / Approach:
We translate the condition "Mathematics marks are 60 percent of the total of both subjects" into an equation. Percentages are converted to decimals for easier computation. This gives a linear equation in a single variable S. Solving this equation yields Pranita's Science marks, and then Mathematics marks can also be checked if desired.

Step-by-Step Solution:
Step 1: Let Science marks = S.Step 2: Mathematics marks = S + 30, since she scores 30 more in Mathematics.Step 3: Sum of both subjects = S (Science) + (S + 30) (Mathematics) = 2S + 30.Step 4: Given that Mathematics marks are 60 percent of the total, we write: S + 30 = 0.60 * (2S + 30).Step 5: Expand the right side: 0.60 * (2S + 30) = 1.2S + 18.Step 6: So, the equation becomes S + 30 = 1.2S + 18.Step 7: Rearrange to solve: S - 1.2S = 18 - 30, which gives -0.2S = -12.Step 8: Divide both sides by -0.2: S = -12 / -0.2 = 60.

Verification / Alternative check:
If Science marks S = 60, then Mathematics marks are S + 30 = 90. The total marks in both subjects are 60 + 90 = 150. Sixty percent of 150 is 0.60 * 150 = 90, which matches the Mathematics marks. This confirms that S = 60 and M = 90 satisfy the given condition completely.

Why Other Options Are Wrong:
- 90 or 120 as Science marks would produce totals and percentages that do not satisfy the condition that Mathematics marks are 60 percent of the combined total.
- 150 as Science marks is impossible when Mathematics is only 30 marks higher, because then Mathematics would be 180 and 60 percent of their sum would not equal 180.

Common Pitfalls:
A typical mistake is to treat 60 percent as a fraction of only one subject instead of the combined total, or to misunderstand "60 percent of the sum" as some other relationship. Another error is to forget to form the correct equation S + 30 = 0.60 * (2S + 30) and instead equate wrong expressions. Carefully translate each part of the verbal statement before solving.

Final Answer:
Pranita's Science marks are 60.