The present average age of family of four members is 36 years . If the present age of the youngest member of family be 12 years , the average age of the family at the birth of the youngest number was

Options

A. 48 years
B. 40 years
C. 32 years
D. 24 years

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total present age of the family
The average age of the family is given as 36 years, and there are 4 members in the family.

\[ \text{Total present age} = \text{Average age} \times \text{Number of members} = 36 \times 4 = 144 \text{ years} \]

**Hint:** To find the total age of a group, multiply the average age by the number of members.

### Step 2: Determine the age of the youngest member
The present age of the youngest member is given as 12 years.

### Step 3: Calculate the total age of the family when the youngest member was born
When the youngest member was born, that was 12 years ago. Thus, we need to subtract the age of all family members at that time. Since there are 4 members, we subtract 12 years from each of the 4 members:

\[ \text{Total age of family 12 years ago} = \text{Total present age} - (4 \times 12) = 144 - 48 = 96 \text{ years} \]

**Hint:** To find the total age at a previous time, subtract the total number of years that have passed from the current total age.

### Step 4: Calculate the average age of the family at that time
Now, we need to find the average age of the family 12 years ago. At that time, there were still 4 members in the family:

\[ \text{Average age 12 years ago} = \frac{\text{Total age 12 years ago}}{\text{Number of members}} = \frac{96}{4} = 24 \text{ years} \]

**Hint:** To find the average age, divide the total age by the number of members.

### Conclusion
The average age of the family at the birth of the youngest member was 24 years.

**Final Answer:** 24 years