Average age of students of an adult school is 40 years. 120 new students whose average is 32 years joined the school. As a result the average age is decreased by 4 years. The number of students of the school after joining of the new students is
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: \(\boxed{240}\)
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