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

Answer

To find the teacher's weight based on the information provided, we can follow these steps:

### 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 can use the formula:

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

Substituting the values:

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

### 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, making the new average:

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

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

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

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 with the teacher:

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

Substituting the values:

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

Thus, the teacher's weight is **86 kg**.