A student obtained 60, 75 and 85 marks respectively in three monthly examinations in Physics and 95 marks in the final examination. The three monthly examinations are of equal weightage whereas the final examination is weighted twice as much as a monthly examination. His average marks in Physics are (a) 78.75 (b) 79 (c) 82 (d) 85

Options

A. 80
B. 81
C. 82
D. 85

Explanation

To find the average marks in Physics for the student, we will follow these steps:

### Step 1: Identify the Marks and Weights
The student obtained the following marks:
- Monthly Examination 1: 60
- Monthly Examination 2: 75
- Monthly Examination 3: 85
- Final Examination: 95

The three monthly examinations have equal weightage, which we will denote as \( x \). The final examination is weighted twice as much, so its weightage will be \( 2x \).

### Step 2: Set Up the Weighted Average Formula
To calculate the average, we will use the formula for weighted average:
\[ \text{Average} = \frac{\text{Total Weighted Marks}}{\text{Total Weightage}} \]

The total weighted marks can be calculated as follows:
\[ \text{Total Weighted Marks} = (60 \times x) + (75 \times x) + (85 \times x) + (95 \times 2x) \]

### Step 3: Simplify the Total Weighted Marks
Now, we can simplify the total weighted marks:
\[ \text{Total Weighted Marks} = 60x + 75x + 85x + 190x \]
\[ = (60 + 75 + 85 + 190)x = 410x \]

### Step 4: Calculate the Total Weightage
Next, we calculate the total weightage:
\[ \text{Total Weightage} = x + x + x + 2x = 5x \]

### Step 5: Calculate the Average
Now, we can substitute the total weighted marks and total weightage into the average formula:
\[ \text{Average} = \frac{410x}{5x} \]

### Step 6: Cancel Out the Common Terms
Since \( x \) is common in both the numerator and denominator, we can cancel it out:
\[ \text{Average} = \frac{410}{5} = 82 \]

### Conclusion
The average marks in Physics are **82**.

### Answer
(c) 82

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