The average weight of a class of 39 students is 40 kg. when a new student is admitted to the class, the averages decreases by 200 g. find the weight of the new student.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total weight of the initial 39 students.
The average weight of the class is given as 40 kg, and there are 39 students.

\[ \text{Total weight of 39 students} = \text{Average weight} \times \text{Number of students} = 40 \, \text{kg} \times 39 = 1560 \, \text{kg} \]

### Step 2: Determine the new average weight after the new student is admitted.
The average weight decreases by 200 grams when a new student is admitted. We need to convert 200 grams to kilograms:

\[ 200 \, \text{grams} = 0.2 \, \text{kg} \]

Thus, the new average weight becomes:

\[ \text{New average} = 40 \, \text{kg} - 0.2 \, \text{kg} = 39.8 \, \text{kg} \]

### Step 3: Calculate the total weight of the 40 students.
Now that we have the new average weight for 40 students, we can calculate the total weight:

\[ \text{Total weight of 40 students} = \text{New average weight} \times \text{New number of students} = 39.8 \, \text{kg} \times 40 = 1592 \, \text{kg} \]

### Step 4: Find the weight of the new student.
To find the weight of the new student, we subtract the total weight of the original 39 students from the total weight of the 40 students:

\[ \text{Weight of new student} = \text{Total weight of 40 students} - \text{Total weight of 39 students} = 1592 \, \text{kg} - 1560 \, \text{kg} = 32 \, \text{kg} \]

### Final Answer:
The weight of the new student is **32 kg**.

---