The average weight of 29 students is 28 kg. by the admission of a new student, the average weight is reduced to 27.8 kg. The weight of the new student is

Options

A. a) 22 kg
B. b) 21.6 kg
C. c) 22.4 kg
D. d) 21 kg

Answer

To find the weight of the new student, we can follow these steps:

### Step 1: Calculate the total weight of the original 29 students.
The average weight of the 29 students is given as 28 kg. To find the total weight, we multiply the average weight by the number of students.

\[ \text{Total weight of 29 students} = \text{Average weight} \times \text{Number of students} = 28 \, \text{kg} \times 29 = 812 \, \text{kg} \]

### Step 2: Calculate the total weight after the new student is admitted.
After the new student is admitted, the average weight of the 30 students becomes 27.8 kg. We can find the new total weight by multiplying the new average weight by the new number of students.

\[ \text{Total weight of 30 students} = \text{New average weight} \times \text{New number of students} = 27.8 \, \text{kg} \times 30 = 834 \, \text{kg} \]

### Step 3: Calculate the weight of the new student.
To find the weight of the new student, we subtract the total weight of the original 29 students from the total weight of the 30 students.

\[ \text{Weight of new student} = \text{Total weight of 30 students} - \text{Total weight of 29 students} = 834 \, \text{kg} - 812 \, \text{kg} = 22 \, \text{kg} \]

### Final Answer:
The weight of the new student is **22 kg**.

---