Study the given information carefully and answer the following questions.
Four students i.e. A, B, C and D appeared for written and practical examinations of year 2019-20
The information given below is known:
Total Maximum Marks = Maximum marks of written Exam + Maximum marks of practical Exam
Total Maximum weighted score = Maximum marks in written exam `xx` weighted % + Maximum marks in practical exam `xx` weighted %
Weighted score = Marks obtained in written exam `xx` weighted % + Marks obtained in practical exam `xx` weighted % Weighted percentage of written exam is 60% and that of practical exam is 40%.
Also, maximum marks of written exam is 80 and that of practical exam is 60
It is given that: Total weighted score of A is 52 . Total weighted score of B is 52 and B obtained 55 marks in practical exam. C obtained 50 marks in practical exam. Marks obtained by D in written examination is 70 and D obtained 75% marks in practical exam.
If D scored `7 1/7` % more marks in written exam and C scored 60 marks in written exam, then find the difference between obtained weighted score of C and D is what percent of total maximum possible weighted score?

Options

A. `8.56%`
B. `9.72%`
C. `10.34%`
D. `7.52%`

Explanation

To solve the problem step by step, we will first summarize the given data and then calculate the required values.

### Step 1: Understand the given data
- Maximum marks in written exam = 80
- Maximum marks in practical exam = 60
- Weighted percentage of written exam = 60% (0.6)
- Weighted percentage of practical exam = 40% (0.4)

### Step 2: Calculate the total maximum possible weighted score
Total maximum possible weighted score = (Maximum marks in written exam × Weighted percentage of written exam) + (Maximum marks in practical exam × Weighted percentage of practical exam)

\[ \text{Total maximum weighted score} = (80 \times 0.6) + (60 \times 0.4) \]
\[ = 48 + 24 = 72 \]

### Step 3: Calculate the weighted scores for students C and D
**For Student C:**
- Marks obtained in practical exam = 50
- Marks obtained in written exam = 60

Weighted score for C:
\[ \text{Weighted score of C} = (60 \times 0.6) + (50 \times 0.4) \]
\[ = 36 + 20 = 56 \]

**For Student D:**
- Marks obtained in written exam = 70
- Marks obtained in practical exam = 75% of 60 = 45

Weighted score for D:
\[ \text{Weighted score of D} = (70 \times 0.6) + (45 \times 0.4) \]
\[ = 42 + 18 = 60 \]

### Step 4: Calculate the difference in weighted scores
Difference between the weighted scores of C and D:
\[ \text{Difference} = \text{Weighted score of D} - \text{Weighted score of C} = 60 - 56 = 4 \]

### Step 5: Calculate the percentage of the difference with respect to the total maximum possible weighted score
\[ \text{Percentage} = \left(\frac{\text{Difference}}{\text{Total maximum weighted score}}\right) \times 100 \]
\[ = \left(\frac{4}{72}\right) \times 100 = \frac{400}{72} \approx 5.56\% \]

### Final Answer
The difference between the obtained weighted score of C and D is approximately **5.56%** of the total maximum possible weighted score.

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