The median and mean values of the marks obtained by the students of a class are 46.67 and 45.5, respectively. Find out the mode of the marks.

Options

A. `60.00`
B. `58.58`
C. `49.01`
D. 40

Answer

To find the mode of the marks obtained by the students in the class, we can use the relationship between the mean, median, and mode. The formula we will use is:

\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Median (M) = 46.67
- Mean (A) = 45.5

2. **Substitute the Values into the Formula:**
\[ \text{Mode} = 3 \times 46.67 - 2 \times 45.5 \]

3. **Calculate \(3 \times \text{Median}\):**
\[ 3 \times 46.67 = 140.01 \]

4. **Calculate \(2 \times \text{Mean}\):**
\[ 2 \times 45.5 = 91.0 \]

5. **Subtract \(2 \times \text{Mean}\) from \(3 \times \text{Median}\):**
\[ \text{Mode} = 140.01 - 91.0 = 49.01 \]

6. **Final Result:**
The mode of the marks is **49.01**.