The average weight of 21 girls was recorded as 58 kg. If a teacher's weight is also added, the average weight increases by 1 kg. What is the weight of the teacher ?

Options

A. 96 kg
B. 78 kg
C. 80 kg
D. 62 kg

Explanation

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

### Step 1: Calculate the total weight of the 21 girls.
The average weight of the 21 girls is given as 58 kg.

To find the total weight of the girls, we can use the formula:
\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Girls} \]
Substituting the values:
\[ \text{Total Weight} = 58 \, \text{kg} \times 21 = 1218 \, \text{kg} \]

### Step 2: Determine the new average weight when the teacher is included.
When the teacher's weight is added, the average weight increases by 1 kg. Therefore, the new average weight is:
\[ \text{New Average Weight} = 58 \, \text{kg} + 1 \, \text{kg} = 59 \, \text{kg} \]

### Step 3: Calculate the total weight of the 22 individuals (21 girls + 1 teacher).
Now, we can find the total weight when the teacher is included. The total number of individuals is now 22 (21 girls + 1 teacher). Using the new average weight:
\[ \text{Total Weight with Teacher} = \text{New Average Weight} \times \text{Total Number of Individuals} \]
Substituting the values:
\[ \text{Total Weight with Teacher} = 59 \, \text{kg} \times 22 = 1298 \, \text{kg} \]

### Step 4: Calculate the weight of the teacher.
Now, we can find the weight of the teacher by subtracting the total weight of the girls from the total weight with the teacher:
\[ \text{Weight of Teacher} = \text{Total Weight with Teacher} - \text{Total Weight of Girls} \]
Substituting the values:
\[ \text{Weight of Teacher} = 1298 \, \text{kg} - 1218 \, \text{kg} = 80 \, \text{kg} \]

### Conclusion:
The weight of the teacher is **80 kg**.

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