In a class, there are 40 boys and their average age is 16 years. One boy, ages 17 years, leaving the class and another joining, the average age becomes 15.875 years. The age of the new boys is :

Options

A. 12
B. 14.5
C. 15
D. 17

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total age of the boys before the change
Given that there are 40 boys and their average age is 16 years, we can find the total age of all boys in the class.

\[ \text{Total age of boys} = \text{Number of boys} \times \text{Average age} = 40 \times 16 = 640 \text{ years} \]

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

### Step 2: Account for the boy leaving
When one boy aged 17 years leaves the class, we need to subtract his age from the total age.

\[ \text{New total age} = 640 - 17 = 623 \text{ years} \]

**Hint:** When someone leaves a group, subtract their contribution (age) from the total.

### Step 3: Calculate the new total age after the new boy joins
Let the age of the new boy be \( x \). After the new boy joins, the total age becomes:

\[ \text{Total age after new boy joins} = 623 + x \]

**Hint:** When a new member joins, add their contribution (age) to the total.

### Step 4: Set up the equation for the new average
The average age after the new boy joins is given as 15.875 years. Since there are still 40 boys in the class, we can set up the equation:

\[ \frac{623 + x}{40} = 15.875 \]

**Hint:** The average is calculated by dividing the total age by the number of individuals.

### Step 5: Solve for \( x \)
To eliminate the fraction, multiply both sides of the equation by 40:

\[ 623 + x = 15.875 \times 40 \]

Calculating the right side:

\[ 15.875 \times 40 = 635 \]

Now, we have:

\[ 623 + x = 635 \]

Subtract 623 from both sides to find \( x \):

\[ x = 635 - 623 = 12 \]

**Hint:** To isolate the variable, perform inverse operations (subtracting in this case).

### Conclusion
The age of the new boy is \( 12 \) years.

**Final Answer:** The age of the new boy is 12 years.