Step-by-step Solution:

Let’s solve the problem step by step.

1. Let \( n \) be the original number of students. The total age of the original students is \( 40n \).

2. 120 new students join with an average age of 32. Their total age is \( 120 \times 32 = 3840 \).

3. After joining, the total number of students becomes \( n + 120 \), and the total age becomes \( 40n + 3840 \).

4. The new average age is \( 40 - 4 = 36 \). So: \[ \frac{40n + 3840}{n + 120} = 36 \] 5. Solve the equation: \[ 40n + 3840 = 36(n + 120) \] \[ 40n + 3840 = 36n + 4320 \] \[ 4n = 480 \] \[ n = 120 \] 6. The total number of students after joining is: \[ 120 + 120 = 240 \] Final Answer: \(\boxed{240}\)