In a particular school, out of total 640 boys that include all the age-groups, 60% of the boys below 18 were enrolled. Out of them, 50% attended the school irregularly. If 120 boys among them were regular, how many boys were there in the school who are above 18?

Understanding the Problem

We are given the following information about a school:
– There are a total of 640 boys in the school.
– 60% of the boys below 18 years old were enrolled.
– Out of the enrolled boys below 18, 50% attended the school irregularly.
– Among the enrolled boys below 18, 120 were regular attendees.

We need to find out how many boys in the school are above 18 years old.

Solving the Problem

Let’s denote the number of boys below 18 years old as \( B_{\text{below 18}} \).

According to the problem, 60% of these boys were enrolled, so the number of enrolled boys below 18 is:

\[ E_{\text{below 18}} = 0.60 \times B_{\text{below 18}} \]

Out of these enrolled boys, 50% attended the school irregularly, so the number of regular attendees is:

\[ R_{\text{below 18}} = 0.50 \times E_{\text{below 18}} \]

But we know that there were 120 regular attendees, so:

\[ R_{\text{below 18}} = 120 = 0.50 \times E_{\text{below 18}} \]

Solving for \( E_{\text{below 18}} \):

\[ E_{\text{below 18}} = \frac{120}{0.50} = 240 \]

Now, we can find \( B_{\text{below 18}} \) using the equation:

\[ B_{\text{below 18}} = \frac{E_{\text{below 18}}}{0.60} = \frac{240}{0.60} = 400 \]

Since there are a total of 640 boys in the school, the number of boys above 18 years old is:

\[ B_{\text{above 18}} = \text{Total boys} – B_{\text{below 18}} = 640 – 400 = 240 \]

Conclusion

There are 240 boys in the school who are above 18 years old.