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 the average marks of A, B, C and D in the practical exam is 47.5 and both A and C scored equal marks in written exam, then what is the average weighted scores of C and D?

Options

A. 56
B. 58
C. 60
D. 52

Explanation

To find the average weighted scores of students C and D, we will follow these steps:

### Step 1: Calculate Marks of A in Practical Exam
Given that the average marks of A, B, C, and D in the practical exam is 47.5, we can find the total marks obtained in the practical exam by all four students:

\[ \text{Total marks in Practical Exam} = \text{Average} \times \text{Number of Students} = 47.5 \times 4 = 190 \]

We know the marks obtained by B, C, and D:
- B = 55
- C = 50
- D = 75% of 60 = 45

Now, we can find A's marks in the practical exam:

\[ A + B + C + D = 190 \implies A + 55 + 50 + 45 = 190 \]
\[ A + 150 = 190 \implies A = 190 - 150 = 40 \]

### Step 2: Calculate Marks of A in Written Exam
We know that the total weighted score of A is 52. The formula for the weighted score is:

\[ \text{Weighted Score} = \left(\text{Marks in Written Exam} \times 0.6\right) + \left(\text{Marks in Practical Exam} \times 0.4\right) \]

Let \( Y \) be the marks obtained by A in the written exam. Then:

\[ 52 = (Y \times 0.6) + (40 \times 0.4) \]
\[ 52 = 0.6Y + 16 \]
\[ 0.6Y = 52 - 16 = 36 \implies Y = \frac{36}{0.6} = 60 \]

### Step 3: Marks of C in Written Exam
Since A and C scored equal marks in the written exam, C also scored 60 marks in the written exam.

### Step 4: Calculate Weighted Score of C
Now we can calculate the weighted score of C:

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

### Step 5: Calculate Weighted Score of D
Next, we calculate the weighted score of D. We know:
- Marks in Written Exam = 70
- Marks in Practical Exam = 45

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

### Step 6: Calculate Average Weighted Score of C and D
Finally, we find the average of the weighted scores of C and D:

\[ \text{Average Weighted Score} = \frac{\text{Weighted Score of C} + \text{Weighted Score of D}}{2} \]
\[ = \frac{56 + 60}{2} = \frac{116}{2} = 58 \]

### Final Answer
The average weighted scores of C and D is **58**.

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