Average weight of 25 students of a class is 50 kg. If the weight of the class teacher is included, the average is increased by 1 kg. The weight of the teacher is:

Options

A. 76 kg
B. 77 kg
C. 74 kg
D. 75 kg

Answer

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

### Step 1: Calculate the total weight of the 25 students.
The average weight of the 25 students is given as 50 kg.

To find the total weight of the students, we use the formula:
\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Students} \]
\[ \text{Total Weight} = 50 \, \text{kg} \times 25 = 1250 \, \text{kg} \]

### Step 2: Determine the new average weight when the teacher is included.
When the teacher's weight is included, the average weight increases by 1 kg, making the new average weight:
\[ \text{New Average Weight} = 50 \, \text{kg} + 1 \, \text{kg} = 51 \, \text{kg} \]

### Step 3: Calculate the total weight of the class including the teacher.
Now, there are 26 individuals (25 students + 1 teacher). We can find the total weight of the class (students + teacher) using the new average:
\[ \text{Total Weight with Teacher} = \text{New Average Weight} \times \text{Total Number of Individuals} \]
\[ \text{Total Weight with Teacher} = 51 \, \text{kg} \times 26 = 1326 \, \text{kg} \]

### Step 4: Calculate the weight of the teacher.
To find the weight of the teacher, we subtract the total weight of the students from the total weight including the teacher:
\[ \text{Weight of Teacher} = \text{Total Weight with Teacher} - \text{Total Weight of Students} \]
\[ \text{Weight of Teacher} = 1326 \, \text{kg} - 1250 \, \text{kg} = 76 \, \text{kg} \]

### Conclusion:
The weight of the teacher is **76 kg**.

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