The average age of a family of 10 members is 20 years. If the age of the youngest member of the family Is 10 years, then the average age of the members of the family Just before the birth of the youngest member was approximately

Options

A. 27.14 years
B. 12.5 years
C. 14.28 years
D. `11 (1/9)` years

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript:

### Step 1: Calculate the total age of the family members.
The average age of the family is given as 20 years, and there are 10 members in the family.

\[ \text{Total Age} = \text{Average Age} \times \text{Number of Members} = 20 \times 10 = 200 \text{ years} \]

**Hint:** To find the total age when the average and number of members are known, multiply the average age by the number of members.

### Step 2: Determine the total age of the family members 10 years ago.
Since the youngest member is currently 10 years old, we can deduce that 10 years ago, the youngest member did not exist. Therefore, the ages of the remaining 9 members would have been 10 years younger than their current ages.

\[ \text{Total Age 10 years ago} = \text{Total Age Now} - (\text{Number of Members} \times \text{Years Ago}) = 200 - (10 \times 10) = 200 - 100 = 100 \text{ years} \]

**Hint:** To find the total age of the family members at a previous time, subtract the total age lost due to the passage of time from the current total age.

### Step 3: Calculate the average age of the family members just before the youngest member was born.
At that time, there were only 9 members in the family (since the youngest member had not yet been born).

\[ \text{Average Age Just Before Birth} = \frac{\text{Total Age 10 years ago}}{\text{Number of Members Just Before Birth}} = \frac{100}{9} \approx 11.11 \text{ years} \]

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

### Final Answer:
The average age of the family members just before the birth of the youngest member was approximately \( 11.11 \) years.