Average age of 5 boy is 16 yr, of which that of 4 boys is 16 yr 3 months. The age of the 5th boy is

Options

A. 15yr
B. 15yr 6 months
C. 15yr 4 months
D. 15yr 2months

Answer

To find the age of the 5th boy, we can follow these steps:

### Step 1: Calculate the total age of the 5 boys.
The average age of the 5 boys is given as 16 years. The formula for average is:

\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of boys}} \]

So, we can rearrange the formula to find the sum of ages:

\[ \text{Sum of ages} = \text{Average} \times \text{Number of boys} \]

Substituting the values:

\[ \text{Sum of ages} = 16 \text{ years} \times 5 = 80 \text{ years} \]

### Step 2: Calculate the total age of the 4 boys.
The average age of the 4 boys is given as 16 years 3 months. First, we need to convert 16 years 3 months into years:

\[ 16 \text{ years} + \frac{3 \text{ months}}{12} = 16 + 0.25 = 16.25 \text{ years} \]

Now, we can calculate the sum of the ages of the 4 boys:

\[ \text{Sum of ages of 4 boys} = 16.25 \text{ years} \times 4 = 65 \text{ years} \]

### Step 3: Calculate the age of the 5th boy.
Now that we have the total age of all 5 boys and the total age of the 4 boys, we can find the age of the 5th boy by subtracting the sum of the ages of the 4 boys from the sum of the ages of the 5 boys:

\[ \text{Age of 5th boy} = \text{Sum of ages of 5 boys} - \text{Sum of ages of 4 boys} \]

Substituting the values:

\[ \text{Age of 5th boy} = 80 \text{ years} - 65 \text{ years} = 15 \text{ years} \]

### Final Answer:
The age of the 5th boy is **15 years**.

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