The average height of four girls was recorded as 150 cms. If the average of the heights of three girls out of the four was 148 cms, what was the height of the fourth girl ?

Options

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

Answer

To find the height of the fourth girl, we can follow these steps:

1. **Calculate the total height of the four girls**:
The average height of the four girls is given as 150 cm. The formula for average is:
\[ \text{Average} = \frac{\text{Total Height}}{\text{Number of Girls}} \]
Therefore, we can rearrange this to find the total height:
\[ \text{Total Height} = \text{Average} \times \text{Number of Girls} = 150 \, \text{cm} \times 4 = 600 \, \text{cm} \]

2. **Calculate the total height of the three girls**:
The average height of three girls is given as 148 cm. Using the same formula:
\[ \text{Total Height of 3 Girls} = \text{Average} \times \text{Number of Girls} = 148 \, \text{cm} \times 3 = 444 \, \text{cm} \]

3. **Find the height of the fourth girl**:
To find the height of the fourth girl, we subtract the total height of the three girls from the total height of all four girls:
\[ \text{Height of 4th Girl} = \text{Total Height of 4 Girls} - \text{Total Height of 3 Girls} = 600 \, \text{cm} - 444 \, \text{cm} = 156 \, \text{cm} \]

Thus, the height of the fourth girl is **156 cm**.