At wharton School every student is awarded with the grades A,B or C only. 57.1428571428 ………% students obtained 'A' grade while 26.4444….% students obtained 'B' grade. If there are less than 3500 students then the maximum number of students obtained the grade 'C' while no one is declared fail.

Options

A. 517
B. 533
C. 428
D. can't be determined

Answer

To solve the problem, we need to determine the maximum number of students who received a grade 'C' at Wharton School, given the percentages of students who received grades 'A' and 'B'.

### Step-by-Step Solution:

1. **Understanding the Given Percentages:**
- Percentage of students who obtained 'A' grade = 57.1428571428...%
- Percentage of students who obtained 'B' grade = 26.4444...%

2. **Setting Up the Equation:**
- Let the percentage of students who obtained 'C' grade be \( X \).
- According to the problem, the total percentage of students must equal 100%.
- Therefore, we can write the equation:
\[ 57.1428571428 + 26.4444 + X = 100 \]

3. **Calculating \( X \):**
- First, we need to add the percentages of 'A' and 'B':
\[ 57.1428571428 + 26.4444 = 83.5872571428 \]
- Now, we can find \( X \):
\[ X = 100 - 83.5872571428 = 16.4127428572 \]

4. **Finding the Total Number of Students:**
- Let \( N \) be the total number of students.
- We know that \( N < 3500 \).
- The number of students who received grade 'C' can be expressed as:
\[ \text{Number of students with grade 'C'} = \frac{X}{100} \times N \]
- Substituting \( X \):
\[ \text{Number of students with grade 'C'} = \frac{16.4127428572}{100} \times N \]

5. **Maximizing the Number of Students with Grade 'C':**
- To maximize the number of students with grade 'C', we should take the maximum possible value of \( N \), which is 3499 (since \( N < 3500 \)).
- Therefore:
\[ \text{Number of students with grade 'C'} = \frac{16.4127428572}{100} \times 3499 \]
- Calculating this:
\[ \text{Number of students with grade 'C'} = 0.164127428572 \times 3499 \approx 574.5 \]
- Since the number of students must be a whole number, we round down to 574.

6. **Final Result:**
- The maximum number of students who obtained grade 'C' is **574**.