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 ratio of marks scored by a 5th student X in the written exam and practical exam is 5 : 3 and the weighted score of X is 52.5, then what is the sum of the marks scored by X in written and practical exams?

Options

A. 96
B. 98
C. 100
D. 92

Explanation

To solve the problem step-by-step, we will follow the information provided and apply the necessary calculations.

### Step 1: Understand the Ratio of Marks
The ratio of marks scored by student X in the written exam to the practical exam is given as 5:3. We can express the marks obtained in the written exam and practical exam in terms of a variable \( a \):
- Marks obtained in written exam = \( 5a \)
- Marks obtained in practical exam = \( 3a \)

### Step 2: Set Up the Weighted Score Equation
The weighted score for student X is given as 52.5. The formula for the weighted score is:
\[ \text{Weighted Score} = (\text{Marks in Written Exam} \times \text{Weighted Percentage of Written Exam}) + (\text{Marks in Practical Exam} \times \text{Weighted Percentage of Practical Exam}) \]
Substituting the known values:
\[ 52.5 = (5a \times 0.6) + (3a \times 0.4) \]

### Step 3: Simplify the Equation
Now we will simplify the equation:
\[ 52.5 = (3a) + (1.2a) \]
Combining like terms gives:
\[ 52.5 = 4.2a \]

### Step 4: Solve for \( a \)
To find the value of \( a \), we divide both sides by 4.2:
\[ a = \frac{52.5}{4.2} \]
Calculating this gives:
\[ a = 12.5 \]

### Step 5: Calculate Marks Obtained by X
Now we can find the actual marks obtained by student X:
- Marks in written exam = \( 5a = 5 \times 12.5 = 62.5 \)
- Marks in practical exam = \( 3a = 3 \times 12.5 = 37.5 \)

### Step 6: Find the Sum of Marks
Finally, we need to find the sum of the marks scored by X in both exams:
\[ \text{Total Marks} = \text{Marks in Written Exam} + \text{Marks in Practical Exam} = 62.5 + 37.5 = 100 \]

### Final Answer
The sum of the marks scored by student X in the written and practical exams is **100**.

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