The average age of 6 brothers is 15 years. The age of the youngest brother is 5 years. What was the average age (in years) of the group of brothers at the time of birth of the youngest brother?

Options

A. (A) 14
B. (B) 15
C. (C) 12.5
D. (D) 12

Answer

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

### Step 1: Calculate the total age of the 6 brothers.
Given that the average age of the 6 brothers is 15 years, we can find the total age of all brothers combined.

\[ \text{Total age of 6 brothers} = \text{Average age} \times \text{Number of brothers} = 15 \times 6 = 90 \text{ years} \]

**Hint:** To find the total age from the average, multiply the average age by the number of individuals.

### Step 2: Determine the total age of the 5 older brothers.
We know the age of the youngest brother is 5 years. Therefore, the total age of the other 5 brothers can be calculated by subtracting the age of the youngest brother from the total age.

\[ \text{Total age of 5 older brothers} = \text{Total age of 6 brothers} - \text{Age of youngest brother} = 90 - 5 = 85 \text{ years} \]

**Hint:** When you know the total and one part, you can find the other part by subtraction.

### Step 3: Calculate the age of the 5 older brothers at the time of the youngest brother's birth.
At the time of the youngest brother's birth, he was not yet born, which means all the older brothers were 5 years younger than they are now. Therefore, we need to subtract 5 years from the total age of the 5 older brothers.

\[ \text{Total age of 5 older brothers at the time of birth} = 85 - (5 \times 5) = 85 - 25 = 60 \text{ years} \]

**Hint:** When considering a past event, adjust the ages by subtracting the number of years since that event.

### Step 4: Calculate the average age of the 5 older brothers at that time.
Now that we have the total age of the 5 older brothers at the time of the youngest brother's birth, we can find their average age.

\[ \text{Average age of 5 older brothers at the time of birth} = \frac{\text{Total age of 5 older brothers at birth}}{\text{Number of older brothers}} = \frac{60}{5} = 12 \text{ years} \]

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

### Final Answer:
The average age of the group of brothers at the time of the birth of the youngest brother was **12 years**.