The average weight of 100 students is 32 kg. The average weight of first 49 students is 30 kg and that of last 50 students is 34 kg. What is the weight (in kg) of the 50th student?

Options

A. 25
B. 30
C. 32
D. 33

Answer

To find the weight of the 50th student, we can follow these steps:

### Step 1: Calculate the total weight of all 100 students.
The average weight of 100 students is given as 32 kg. Therefore, the total weight of all 100 students can be calculated as:
\[ \text{Total weight of 100 students} = \text{Average weight} \times \text{Number of students} = 32 \, \text{kg} \times 100 = 3200 \, \text{kg} \]

### Step 2: Calculate the total weight of the first 49 students.
The average weight of the first 49 students is given as 30 kg. Therefore, the total weight of the first 49 students can be calculated as:
\[ \text{Total weight of first 49 students} = 30 \, \text{kg} \times 49 = 1470 \, \text{kg} \]

### Step 3: Calculate the total weight of the last 50 students.
The average weight of the last 50 students is given as 34 kg. Therefore, the total weight of the last 50 students can be calculated as:
\[ \text{Total weight of last 50 students} = 34 \, \text{kg} \times 50 = 1700 \, \text{kg} \]

### Step 4: Set up the equation to find the weight of the 50th student.
Let the weight of the 50th student be \( x \) kg. The total weight of the last 50 students includes the weight of the 50th student, so we can express it as:
\[ \text{Total weight of last 50 students} = \text{Weight of 49 students} + \text{Weight of 50th student} \]
This gives us:
\[ 1470 + x = 1700 \]

### Step 5: Solve for \( x \).
Now, we can solve for \( x \):
\[ x = 1700 - 1470 = 230 \, \text{kg} \]

### Step 6: Verify the total weight.
To ensure our calculations are correct, we can verify by checking if the total weight of all students matches:
\[ \text{Total weight of all students} = \text{Weight of first 49 students} + \text{Weight of last 50 students} \]
This gives us:
\[ 1470 + 1700 = 3200 \, \text{kg} \]
This confirms that our calculations are correct.

### Final Answer:
The weight of the 50th student is \( 230 \, \text{kg} \).