The average age of a class is 21 years. If a student with age 42 years joins the class, then new average age becomes 24 years. How many total students are there in the class?

Options

A. a. 5
B. b. 7
C. c. 8
D. d. 6

Answer

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

1. **Let the number of students in the class be \( x \)**.
- This is our starting point to represent the unknown number of students.

2. **Calculate the total age of the students in the class**.
- The average age of the class is given as 21 years. Therefore, the total age of all students can be expressed as:
\[ \text{Total age} = \text{Average age} \times \text{Number of students} = 21x \]

3. **When a new student aged 42 years joins the class**, the new total age becomes:
\[ \text{New total age} = 21x + 42 \]

4. **The new number of students in the class becomes \( x + 1 \)**.

5. **The new average age is given as 24 years**. We can set up the equation for the new average:
\[ \frac{21x + 42}{x + 1} = 24 \]

6. **Cross-multiply to eliminate the fraction**:
\[ 21x + 42 = 24(x + 1) \]

7. **Expand the right-hand side**:
\[ 21x + 42 = 24x + 24 \]

8. **Rearrange the equation to isolate \( x \)**:
\[ 21x + 42 - 24 = 24x \]
\[ 21x + 18 = 24x \]

9. **Subtract \( 21x \) from both sides**:
\[ 18 = 24x - 21x \]
\[ 18 = 3x \]

10. **Divide both sides by 3 to solve for \( x \)**:
\[ x = \frac{18}{3} = 6 \]

11. **Thus, the total number of students in the class is \( x + 1 \)** (including the new student):
\[ \text{Total students} = 6 + 1 = 7 \]

**Final Answer**: There are 7 students in the class.