Simplify the sum of the mixed fractions 4 1/3, 2 1/5 and 4 1/4, and express your final answer as a mixed fraction in simplest form.

Introduction / Context:
This question tests basic fraction skills, especially handling mixed fractions. You must convert mixed numbers to improper fractions, add them, and then convert back to a mixed fraction if required. Operations like this are common in school mathematics and form the foundation for more advanced fraction and ratio calculations in aptitude exams.

Given Data / Assumptions:

• The three mixed fractions are 4 1/3, 2 1/5, and 4 1/4.
• We are required to find their sum.
• The final answer must be expressed as a mixed fraction in simplest form.

Concept / Approach:
Mixed fractions are easier to add if we first convert them to improper fractions. An improper fraction has the form (whole * denominator + numerator) over the denominator. Once converted, we add the fractions by finding a common denominator. After obtaining the final improper fraction, we simplify it if possible and then convert it back to a mixed fraction for a more intuitive interpretation.

Step-by-Step Solution:
First convert each mixed fraction to an improper fraction. 4 1/3 = (4 * 3 + 1) / 3 = 13/3. 2 1/5 = (2 * 5 + 1) / 5 = 11/5. 4 1/4 = (4 * 4 + 1) / 4 = 17/4. We now add 13/3 + 11/5 + 17/4. The denominators are 3, 5, and 4. A convenient common denominator is 60. Convert each fraction to denominator 60. 13/3 = (13 * 20) / 60 = 260/60. 11/5 = (11 * 12) / 60 = 132/60. 17/4 = (17 * 15) / 60 = 255/60. Now add the numerators: 260 + 132 + 255 = 647. So the sum is 647/60. Convert 647/60 to a mixed fraction. Divide 647 by 60: 60 * 10 = 600, remainder 47. So, 647/60 = 10 47/60.

Verification / Alternative check:
We can also add the whole number parts and fractional parts separately as a quick check. Whole parts: 4 + 2 + 4 = 10. Fractional parts: 1/3 + 1/5 + 1/4. Convert to denominator 60: 1/3 = 20/60, 1/5 = 12/60, 1/4 = 15/60. Sum of fractional parts = 20/60 + 12/60 + 15/60 = 47/60. Thus the total is 10 and 47/60, confirming the result obtained earlier.

Why Other Options Are Wrong:
11 45/73 and 11 47/36: These fractions have incorrect denominators and do not come from any reasonable common denominator of 3, 5, and 4.
10 35/48: The denominator 48 does not match the least common multiple of 3, 5, and 4, which is 60, and the numerator 35 is also inconsistent with the correct sum of fractional parts.
9 7/8: This value is less than 10, whereas the sum of whole parts alone is already 10, so it cannot be correct.

Common Pitfalls:
Common mistakes include miscalculating the improper fraction representation, choosing an incorrect common denominator, or adding the numerators incorrectly. Some students also forget to simplify the final fraction or convert it back to a mixed number. Working in an organised way, either by converting everything to a common denominator or by separately summing whole and fractional parts, helps avoid these problems.

Final Answer:
The simplified sum of the three mixed fractions is 10 47/60.