A candidate obtains the marks in subjects English 60 Hindi 75 , Mathematics 63 , Physics 59 and Chemistry 55 . In the weights of 1,2,1,3,3 respectively are alloted to the subjects then the candidates weighted mean is

Options

A. `59`
B. `615`
C. `10`
D. `61.5`

Answer

To find the weighted mean of the candidate's marks in different subjects, we will follow these steps:

### Step 1: List the Marks and Weights
We have the following marks and their corresponding weights:

- English: Marks = 60, Weight = 1
- Hindi: Marks = 75, Weight = 2
- Mathematics: Marks = 63, Weight = 1
- Physics: Marks = 59, Weight = 3
- Chemistry: Marks = 55, Weight = 3

### Step 2: Calculate the Total Weight
The total weight (N) is calculated by summing the weights of all subjects:

\[ N = 1 + 2 + 1 + 3 + 3 = 10 \]

### Step 3: Calculate the Weighted Marks
Next, we calculate the weighted marks for each subject by multiplying the marks by their respective weights:

- English: \(60 \times 1 = 60\)
- Hindi: \(75 \times 2 = 150\)
- Mathematics: \(63 \times 1 = 63\)
- Physics: \(59 \times 3 = 177\)
- Chemistry: \(55 \times 3 = 165\)

### Step 4: Sum the Weighted Marks
Now, we sum all the weighted marks:

\[ \text{Total Weighted Marks} = 60 + 150 + 63 + 177 + 165 = 615 \]

### Step 5: Calculate the Weighted Mean
Finally, we calculate the weighted mean using the formula:

\[ \text{Weighted Mean} = \frac{\text{Total Weighted Marks}}{N} = \frac{615}{10} = 61.5 \]

### Conclusion
The candidate's weighted mean is **61.5**.

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