In aptitude (fractions and percentages simplification), simplify the following equation with mixed numbers and percentages and find the missing value represented by '?' in (4 1/5) * (3 1/3) + ? = 20% of 120.

Introduction / Context:
This question combines basic operations on mixed numbers, multiplication of fractions, and percentage calculation. Such simplification questions are very common in bank exams, SSC, and other competitive tests. The goal is to carefully convert mixed numbers into improper fractions, multiply them correctly, and then compare the result with a percentage of a whole number to find the missing value represented by the symbol '?'. Accuracy with fractions and percentages is crucial here.

Given Data / Assumptions:
- Expression: (4 1/5) * (3 1/3) + ? = 20% of 120.
- Mixed numbers 4 1/5 and 3 1/3 should be converted to improper fractions.
- Percentage 20% of 120 means 20/100 * 120.
- Operations are standard arithmetic under real numbers.

Concept / Approach:
The concept is straightforward: first evaluate the left part without the unknown, that is (4 1/5) * (3 1/3). Then compute the right side, which is 20% of 120. Once both values are computed, treat the equation as A + ? = B and solve for the missing value ? = B - A. Careful conversion and simplification of fractions will make the arithmetic cleaner and reduce chances of mistakes.

Step-by-Step Solution:
Step 1: Convert 4 1/5 to an improper fraction: 4 1/5 = (4 * 5 + 1) / 5 = 21 / 5.Step 2: Convert 3 1/3 to an improper fraction: 3 1/3 = (3 * 3 + 1) / 3 = 10 / 3.Step 3: Multiply the fractions: (21 / 5) * (10 / 3) = (21 * 10) / (5 * 3) = 210 / 15 = 14.Step 4: Compute the right-hand side: 20% of 120 = (20 / 100) * 120 = 0.2 * 120 = 24.Step 5: Set up the equation: 14 + ? = 24.Step 6: Rearrange to find ?: ? = 24 - 14 = 10.

Verification / Alternative check:
We can verify quickly by substituting the found value of ? back into the original expression. If ? = 10, then the left side is 14 + 10 = 24. The right side is 20% of 120, which is also 24. Since both sides match exactly, the value ? = 10 is completely consistent and verified.

Why Other Options Are Wrong:
- 12: This would correspond to incorrectly evaluating the mixed number product or miscomputing 20% of 120.
- 14: This may arise if a student mistakenly thinks the product alone equals the percentage result and ignores the role of the unknown term.
- 8: This could result from arithmetic errors such as subtracting in the wrong order (for example, 14 - 24 instead of 24 - 14).
- 16: This might come from miscalculating 20% of 120 as 30 or 14 as a different value, leading to a wrong difference.

Common Pitfalls:
Frequent mistakes include not converting mixed numbers to improper fractions correctly, or incorrectly multiplying the fractions. Some students also compute 20% of 120 as 20 * 120 or 20 / 120 rather than (20 / 100) * 120. Another common error is solving A + ? = B as ? = A - B instead of ? = B - A. Checking each step slowly helps avoid these simple but costly errors in exams.

Final Answer:
The missing value in the equation is 10.