Three year ago, the average age of a family of five members was 27 yr. The persent average age is also 27 yr after the inclusion of a child into the family . Find the age of child .

Options

A. 16yr
B. 12yr
C. 24yr
D. 20yr

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the total age of the family three years ago.
The average age of the family three years ago was 27 years for 5 members.

To find the total age of the family three years ago:
\[ \text{Total age} = \text{Average age} \times \text{Number of members} \]
\[ \text{Total age} = 27 \times 5 = 135 \text{ years} \]

### Step 2: Calculate the total age of the family now.
Since three years have passed, each of the 5 family members has aged 3 years. Therefore, the total increase in age for the 5 members is:
\[ \text{Total increase in age} = 5 \times 3 = 15 \text{ years} \]
Now, we can find the total age of the family now:
\[ \text{Total age now} = \text{Total age three years ago} + \text{Total increase in age} \]
\[ \text{Total age now} = 135 + 15 = 150 \text{ years} \]

### Step 3: Include the child in the family.
Now, a child has been added to the family, and the average age remains 27 years for 6 members (5 original members + 1 child).

To find the total age of the family including the child:
\[ \text{Total age including child} = \text{Average age} \times \text{Number of members} \]
\[ \text{Total age including child} = 27 \times 6 = 162 \text{ years} \]

### Step 4: Calculate the age of the child.
Now, we can find the age of the child by subtracting the total age of the original family from the total age including the child:
\[ \text{Age of child} = \text{Total age including child} - \text{Total age now} \]
\[ \text{Age of child} = 162 - 150 = 12 \text{ years} \]

### Final Answer:
The age of the child is **12 years**.

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