The average age of four boys, five years ago was 9 years. On including a new boy, the present average age of all the five is 15 years. The present age of the new boy is

Options

A. 14 years
B. 6 years
C. 15 years
D. 19 years

Answer

To find the present age of the new boy, we can follow these steps:

### Step 1: Determine the present average age of the four boys
The average age of the four boys five years ago was 9 years. To find their present average age, we add 5 years to the average age from five years ago.

\[ \text{Present average age of four boys} = 9 + 5 = 14 \text{ years} \]

### Step 2: Calculate the total present age of the four boys
Since the average age of the four boys is 14 years, we can find the total present age of the four boys by multiplying the average age by the number of boys.

\[ \text{Total present age of four boys} = 14 \times 4 = 56 \text{ years} \]

### Step 3: Determine the present average age of all five boys
According to the problem, the present average age of all five boys (including the new boy) is 15 years.

### Step 4: Calculate the total present age of all five boys
To find the total present age of all five boys, we multiply the average age by the number of boys.

\[ \text{Total present age of five boys} = 15 \times 5 = 75 \text{ years} \]

### Step 5: Find the present age of the new boy
Now, we can find the present age of the new boy by subtracting the total present age of the four boys from the total present age of all five boys.

\[ \text{Present age of the new boy} = \text{Total present age of five boys} - \text{Total present age of four boys} \]
\[ \text{Present age of the new boy} = 75 - 56 = 19 \text{ years} \]

### Final Answer
The present age of the new boy is **19 years**.

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