The average age of 8 children of a family is 12 year. If age of 7 children are 12, 8, 14, 11, 9, 13 and 15 years respeatively. The age of 8th child is?

Options

A. 12 yr
B. 14 yr
C. 13 yr
D. 15 yr

Answer

To find the age of the 8th child, we can follow these steps:

### Step 1: Understand the average
The average age of 8 children is given as 12 years. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of children}} \]
In this case, we have:
\[ 12 = \frac{\text{Sum of ages of 8 children}}{8} \]

### Step 2: Calculate the total sum of ages
To find the total sum of ages of the 8 children, we can rearrange the formula:
\[ \text{Sum of ages of 8 children} = \text{Average} \times \text{Number of children} = 12 \times 8 = 96 \]

### Step 3: Find the sum of the ages of the first 7 children
The ages of the first 7 children are given as:
12, 8, 14, 11, 9, 13, and 15 years. We will sum these ages:
\[ \text{Sum of ages of 7 children} = 12 + 8 + 14 + 11 + 9 + 13 + 15 \]
Calculating this gives:
\[ 12 + 8 = 20 \\ 20 + 14 = 34 \\ 34 + 11 = 45 \\ 45 + 9 = 54 \\ 54 + 13 = 67 \\ 67 + 15 = 82 \]
So, the sum of the ages of the 7 children is 82 years.

### Step 4: Set up the equation for the 8th child's age
Let the age of the 8th child be \( x \). Therefore, we can write:
\[ \text{Sum of ages of 8 children} = \text{Sum of ages of 7 children} + \text{Age of 8th child} \]
This translates to:
\[ 96 = 82 + x \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = 96 - 82 \\ x = 14 \]
Thus, the age of the 8th child is 14 years.

### Final Answer
The age of the 8th child is **14 years**.

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