The mean weight of 34 students of a school is 42kg . If the weight of the teacher be included , the mean rises by 400 g. find the weight (in kg) of the teacher.

Options

A. 66
B. 56
C. 55
D. 57

Answer

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

### Step 1: Calculate the total weight of the 34 students.
The mean weight of the 34 students is given as 42 kg. To find the total weight of the students, we can use the formula:

\[ \text{Total weight of students} = \text{Number of students} \times \text{Mean weight} \]

Substituting the values:

\[ \text{Total weight of students} = 34 \times 42 = 1428 \text{ kg} \]

### Step 2: Calculate the new mean weight when the teacher's weight is included.
When the teacher's weight is included, the mean weight increases by 400 grams (which is 0.4 kg). Therefore, the new mean weight becomes:

\[ \text{New mean weight} = 42 + 0.4 = 42.4 \text{ kg} \]

### Step 3: Calculate the total weight when the teacher is included.
Now, we have 35 individuals (34 students + 1 teacher). The total weight with the teacher included can be calculated as:

\[ \text{Total weight with teacher} = \text{Number of individuals} \times \text{New mean weight} \]

Substituting the values:

\[ \text{Total weight with teacher} = 35 \times 42.4 = 1484 \text{ kg} \]

### 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 with the teacher:

\[ \text{Weight of teacher} = \text{Total weight with teacher} - \text{Total weight of students} \]

Substituting the values:

\[ \text{Weight of teacher} = 1484 - 1428 = 56 \text{ kg} \]

### Final Answer:
The weight of the teacher is **56 kg**.

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