There are two groups A and B of a class, consisting of 42 and 28 students respectivery. If the average weight of group A is 25 kg and that of group B is 40 kg. Find the average weight of the whole class.

Options

A. 69 kg
B. 31 kg
C. 70 kg
D. 30 kg

Answer

To find the average weight of the whole class consisting of two groups A and B, we can follow these steps:

### Step 1: Calculate the total weight of Group A
The average weight of Group A is given as 25 kg, and the number of students in Group A is 42.

\[ \text{Total weight of Group A} = \text{Average weight} \times \text{Number of students} = 25 \, \text{kg} \times 42 = 1050 \, \text{kg} \]

### Step 2: Calculate the total weight of Group B
The average weight of Group B is given as 40 kg, and the number of students in Group B is 28.

\[ \text{Total weight of Group B} = \text{Average weight} \times \text{Number of students} = 40 \, \text{kg} \times 28 = 1120 \, \text{kg} \]

### Step 3: Calculate the total weight of the whole class
Now, we will add the total weights of both groups to find the total weight of the whole class.

\[ \text{Total weight of the class} = \text{Total weight of Group A} + \text{Total weight of Group B} = 1050 \, \text{kg} + 1120 \, \text{kg} = 2170 \, \text{kg} \]

### Step 4: Calculate the total number of students in the class
Now, we will find the total number of students in the class by adding the number of students in both groups.

\[ \text{Total number of students} = \text{Number of students in Group A} + \text{Number of students in Group B} = 42 + 28 = 70 \]

### Step 5: Calculate the average weight of the whole class
Finally, we will calculate the average weight of the whole class using the total weight and the total number of students.

\[ \text{Average weight of the class} = \frac{\text{Total weight of the class}}{\text{Total number of students}} = \frac{2170 \, \text{kg}}{70} = 31 \, \text{kg} \]

Thus, the average weight of the whole class is **31 kg**.

---