The average age of 30 girls is 13 yr. The average of first 12 girls is 16 yr. Find out the average age of remaining 18 girls?

Options

A. 12 yr
B. 10 yr
C. 16 yr
D. 11 yr

Answer

To solve the problem step by step, we will use the concept of averages and the formula for calculating the average.

### Step 1: Calculate the total age of all 30 girls.
The average age of 30 girls is given as 13 years. We can find the total age of all 30 girls using the formula:

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

Substituting the values:

\[ \text{Total Age} = 13 \times 30 = 390 \text{ years} \]

### Step 2: Calculate the total age of the first 12 girls.
The average age of the first 12 girls is given as 16 years. We can find their total age using the same formula:

\[ \text{Total Age of 12 Girls} = \text{Average Age} \times \text{Number of Girls} \]

Substituting the values:

\[ \text{Total Age of 12 Girls} = 16 \times 12 = 192 \text{ years} \]

### Step 3: Calculate the total age of the remaining 18 girls.
To find the total age of the remaining 18 girls, we subtract the total age of the first 12 girls from the total age of all 30 girls:

\[ \text{Total Age of 18 Girls} = \text{Total Age of 30 Girls} - \text{Total Age of 12 Girls} \]

Substituting the values:

\[ \text{Total Age of 18 Girls} = 390 - 192 = 198 \text{ years} \]

### Step 4: Calculate the average age of the remaining 18 girls.
Now, we can find the average age of the remaining 18 girls using the formula for average:

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

Substituting the values:

\[ \text{Average Age of 18 Girls} = \frac{198}{18} = 11 \text{ years} \]

### Final Answer:
The average age of the remaining 18 girls is **11 years**.

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