In a family of 5 members, the average age at present Is 33 years. The youngest member is 9 years old. The average age of the family Just before the birth of the youngest member was

Options

A. 30 years
B. 29 years
C. 25 years
D. 24 years

Answer

To solve the problem step by step, we will first calculate the total age of the family members at present and then find the average age just before the youngest member was born.

### Step 1: Calculate the total age of the family members at present.
Given that the average age of the family is 33 years and there are 5 members, we can use the formula for average:

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

Rearranging this gives us:

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

Substituting the values:

\[ \text{Total Age} = 33 \times 5 = 165 \text{ years} \]

### Step 2: Calculate the total age of the family members just before the youngest member was born.
The youngest member is currently 9 years old. Therefore, just before the youngest member was born, all 5 members were 9 years younger.

So, we subtract 9 years from the total age:

\[ \text{Total Age Just Before Birth} = \text{Total Age} - 9 = 165 - 9 = 156 \text{ years} \]

### Step 3: Calculate the average age of the family just before the birth of the youngest member.
Now, we need to find the average age of the family just before the youngest member was born. At that time, there were still 5 members in the family.

Using the average formula again:

\[ \text{Average Age Just Before Birth} = \frac{\text{Total Age Just Before Birth}}{\text{Number of Members}} = \frac{156}{5} \]

Calculating this gives:

\[ \text{Average Age Just Before Birth} = 31.2 \text{ years} \]

### Final Answer:
The average age of the family just before the birth of the youngest member was **31.2 years**.

---