Average age of 30 girls is 14yr. If 5 girls of average age of 15yr leave the class, then find the average age of remaining girls.

Options

A. 13.8yr
B. 12.8yr
C. 9yr
D. 14yr

Answer

To find the average age of the remaining girls after 5 girls leave the class, we can follow these steps:

### Step 1: Calculate the total age of all 30 girls.
The average age of the 30 girls is given as 14 years. Therefore, the total age of all the girls can be calculated using the formula:

\[ \text{Total Age} = \text{Average Age} \times \text{Number of Girls} \]

Substituting the values:

\[ \text{Total Age} = 14 \times 30 = 420 \text{ years} \]

### Step 2: Calculate the total age of the 5 girls who leave.
The average age of the 5 girls who leave is given as 15 years. Therefore, the total age of these 5 girls can be calculated similarly:

\[ \text{Total Age of 5 girls} = \text{Average Age} \times \text{Number of Girls} \]

Substituting the values:

\[ \text{Total Age of 5 girls} = 15 \times 5 = 75 \text{ years} \]

### Step 3: Calculate the total age of the remaining girls.
To find the total age of the remaining girls, we subtract the total age of the 5 girls who left from the total age of all the girls:

\[ \text{Total Age of Remaining Girls} = \text{Total Age of All Girls} - \text{Total Age of 5 girls} \]

Substituting the values:

\[ \text{Total Age of Remaining Girls} = 420 - 75 = 345 \text{ years} \]

### Step 4: Calculate the number of remaining girls.
Since 5 girls have left from the original 30 girls, the number of remaining girls is:

\[ \text{Number of Remaining Girls} = 30 - 5 = 25 \]

### Step 5: Calculate the average age of the remaining girls.
Finally, we can find the average age of the remaining girls using the formula:

\[ \text{Average Age of Remaining Girls} = \frac{\text{Total Age of Remaining Girls}}{\text{Number of Remaining Girls}} \]

Substituting the values:

\[ \text{Average Age of Remaining Girls} = \frac{345}{25} = 13.8 \text{ years} \]

### Conclusion
The average age of the remaining girls is **13.8 years**.

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