In a class there are total 70 students. The average weight of 26 girls is 28 kg and average weight of the remaining students is 35 kg. What will be the average weight(in kg) of all 70 students?

Options

A. 32.4 kg
B. 36.8 kg
C. 35.2 kg
D. 34.6 kg

Answer

To solve the problem step by step, we will calculate the total weight of the girls and the remaining students, then find the overall average weight of all students.

### Step 1: Calculate the total weight of the girls.
- The number of girls = 26
- The average weight of the girls = 28 kg

**Total weight of girls = Number of girls × Average weight of girls**
\[ \text{Total weight of girls} = 26 \times 28 = 728 \text{ kg} \]

### Step 2: Calculate the total weight of the remaining students.
- Total number of students = 70
- Number of remaining students = Total students - Number of girls
\[ \text{Number of remaining students} = 70 - 26 = 44 \]
- The average weight of the remaining students = 35 kg

**Total weight of remaining students = Number of remaining students × Average weight of remaining students**
\[ \text{Total weight of remaining students} = 44 \times 35 = 1540 \text{ kg} \]

### Step 3: Calculate the total weight of all students.
**Total weight of all students = Total weight of girls + Total weight of remaining students**
\[ \text{Total weight of all students} = 728 + 1540 = 2268 \text{ kg} \]

### Step 4: Calculate the average weight of all students.
**Average weight = Total weight of all students / Total number of students**
\[ \text{Average weight} = \frac{2268}{70} \approx 32.4 \text{ kg} \]

Thus, the average weight of all 70 students is **32.4 kg**.