The average age of four brothers is 14 years. If their father is also included, the average is increased by 4 years. The age of the father (in years) is:

Options

A. 36
B. 34
C. 40
D. 38

Answer

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

### Step 1: Calculate the total age of the four brothers
Given that the average age of the four brothers is 14 years, we can calculate their total age.

\[ \text{Total age of four brothers} = \text{Average age} \times \text{Number of brothers} = 14 \times 4 = 56 \text{ years} \]

### Step 2: Determine the new average when the father is included
When the father is included, the average age increases by 4 years. Therefore, the new average age is:

\[ \text{New average age} = 14 + 4 = 18 \text{ years} \]

### Step 3: Calculate the total age of the four brothers and the father
Now, we need to find the total age of the four brothers plus the father. Since there are now five individuals (the four brothers and the father), we can calculate the total age as follows:

\[ \text{Total age of four brothers and father} = \text{New average age} \times \text{Number of individuals} = 18 \times 5 = 90 \text{ years} \]

### Step 4: Find the age of the father
We already calculated the total age of the four brothers as 56 years. Now we can find the father's age by subtracting the total age of the brothers from the total age of all five individuals:

\[ \text{Father's age} = \text{Total age of four brothers and father} - \text{Total age of four brothers} = 90 - 56 = 34 \text{ years} \]

### Conclusion
The age of the father is **34 years**.

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