The average weight of 21 boys was recorded as 64 kg. If the weight of the teacher was added, the average increased by one kg. What was the teacher's weight ?

Options

A. 86 kg
B. 64 kg
C. 72 kg
D. 98 kg

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total weight of the 21 boys.
The average weight of the 21 boys is given as 64 kg. To find the total weight of the boys, we use the formula for average:

\[ \text{Average} = \frac{\text{Total Weight}}{\text{Number of Boys}} \]

Rearranging this formula to find the total weight gives us:

\[ \text{Total Weight} = \text{Average} \times \text{Number of Boys} \]

Substituting the values:

\[ \text{Total Weight} = 64 \, \text{kg} \times 21 = 1344 \, \text{kg} \]

### Step 2: Calculate the new average weight when the teacher's weight is added.
When the teacher's weight is added, the average weight increases by 1 kg, making the new average:

\[ \text{New Average} = 64 \, \text{kg} + 1 \, \text{kg} = 65 \, \text{kg} \]

### Step 3: Calculate the total weight of the 21 boys plus the teacher.
Now, with the teacher included, the total number of individuals becomes 22 (21 boys + 1 teacher). We can calculate the total weight with the new average:

\[ \text{Total Weight with Teacher} = \text{New Average} \times \text{Total Number of Individuals} \]

Substituting the values:

\[ \text{Total Weight with Teacher} = 65 \, \text{kg} \times 22 = 1430 \, \text{kg} \]

### Step 4: Calculate the teacher's weight.
To find the teacher's weight, we subtract the total weight of the boys from the total weight including the teacher:

\[ \text{Teacher's Weight} = \text{Total Weight with Teacher} - \text{Total Weight of Boys} \]

Substituting the values:

\[ \text{Teacher's Weight} = 1430 \, \text{kg} - 1344 \, \text{kg} = 86 \, \text{kg} \]

### Conclusion:
The teacher's weight is **86 kg**.

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