The average height of 21 girls was recorded as 148 cm. When the teacher's height was included , the average of their height increased by 1 cm. What was the height of the teacher ?

Options

A. 156 cm
B. 168 cm
C. 170 cm
D. 162 cm

Explanation

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

### Step 1: Calculate the total height of the 21 girls.
Given that the average height of the 21 girls is 148 cm, we can find the total height using the formula for average:

\[ \text{Total height of 21 girls} = \text{Average height} \times \text{Number of girls} \]

\[ \text{Total height of 21 girls} = 148 \, \text{cm} \times 21 = 3108 \, \text{cm} \]

### Step 2: Calculate the new average height when the teacher is included.
When the teacher's height is included, the average height increases by 1 cm, making the new average height:

\[ \text{New average height} = 148 \, \text{cm} + 1 \, \text{cm} = 149 \, \text{cm} \]

### Step 3: Calculate the total height of 22 individuals (21 girls + teacher).
Now, we can find the total height of all 22 individuals (21 girls + teacher) using the new average:

\[ \text{Total height of 22 individuals} = \text{New average height} \times \text{Total number of individuals} \]

\[ \text{Total height of 22 individuals} = 149 \, \text{cm} \times 22 = 3278 \, \text{cm} \]

### Step 4: Calculate the height of the teacher.
The height of the teacher can be found by subtracting the total height of the 21 girls from the total height of the 22 individuals:

\[ \text{Height of the teacher} = \text{Total height of 22 individuals} - \text{Total height of 21 girls} \]

\[ \text{Height of the teacher} = 3278 \, \text{cm} - 3108 \, \text{cm} = 170 \, \text{cm} \]

### Final Answer:
The height of the teacher is **170 cm**.

---