The average age of a group of 4 friends is 36 years. The youngest friend amongst them is 6 years old. What was the average age of the group at the time of the birth of the youngest friend?

Options

A. a. 36 years
B. b. 38 years
C. c. 32 years
D. d. 40 years

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Calculate the total sum of the ages of the 4 friends.
The average age of the 4 friends is given as 36 years. To find the total sum of their ages, we can use the formula:

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

Substituting the values:

\[ \text{Total Sum} = 36 \times 4 = 144 \text{ years} \]

### Step 2: Determine the sum of the ages of the friends 6 years ago.
Since we want to find the average age at the time of the birth of the youngest friend (who is currently 6 years old), we need to calculate the total sum of their ages 6 years ago. Each friend would have been 6 years younger, so we subtract \(6 \times 4\) from the total sum:

\[ \text{Sum 6 Years Ago} = 144 - (6 \times 4) = 144 - 24 = 120 \text{ years} \]

### Step 3: Calculate the average age of the 3 remaining friends 6 years ago.
When the youngest friend was born, there were only 3 friends left. To find the average age of these 3 friends at that time, we divide the sum of their ages by the number of friends:

\[ \text{Average Age} = \frac{\text{Sum 6 Years Ago}}{\text{Number of Friends}} \]

Substituting the values:

\[ \text{Average Age} = \frac{120}{3} = 40 \text{ years} \]

### Final Answer:
The average age of the group at the time of the birth of the youngest friend was **40 years**.

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