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

Options

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

Explanation

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

### Step 1: Calculate the total height of the four girls.
The average height of the four girls is given as 150 cm. To find the total height, we can use the formula:
\[ \text{Total Height} = \text{Average Height} \times \text{Number of Girls} \]
So, the total height of the four girls is:
\[ \text{Total Height} = 150 \, \text{cm} \times 4 = 600 \, \text{cm} \]

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

### Step 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 the four girls:
\[ \text{Height of Fourth Girl} = \text{Total Height of Four Girls} - \text{Total Height of Three Girls} \]
Substituting the values we calculated:
\[ \text{Height of Fourth Girl} = 600 \, \text{cm} - 444 \, \text{cm} = 156 \, \text{cm} \]

### Final Answer:
The height of the fourth girl is **156 cm**.

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