The table below shows the number of girls, the percentage of boys out of the total students, and the percentage of students who attended a seminar in four different schools.

| Schools | Number of girls | Percentage of boys out of total students | Percentage of students attended seminar |
|---------|-----------------|------------------------------------------|-----------------------------------------|
| P | 120 | 40\% | x\% |
| Q | 80 | 80\% | 40\% |
| R | 35 | 65\% | y\% |
| S | 50 | 75\% | 60\% |

Note:
- *x* is 5\% of the average number of students in schools P and Q.
- *y* is 12.5\% of the total students who attended the seminar in school Q.
- Total students = total girls + total boys.
- Total students = students attended seminar + students not attended seminar.

The difference between the number of boys and girls in school R is half the number of girls who attended the seminar in school Q.

Find the ratio of the total boys who attended the seminar in school Q to the total students in schools R and S combined.

Question

The table below shows the number of girls, the percentage of boys out of the total students, and the percentage of students who attended a seminar in four different schools.

| Schools | Number of girls | Percentage of boys out of total students | Percentage of students attended seminar |
|---------|-----------------|------------------------------------------|-----------------------------------------|
| P       | 120             | 40\%                                    | x\%                                    |
| Q       | 80              | 80\%                                    | 40\%                                   |
| R       | 35              | 65\%                                    | y\%                                    |
| S       | 50              | 75\%                                    | 60\%                                   |

Note:
- *x* is 5\% of the average number of students in schools P and Q.
- *y* is 12.5\% of the total students who attended the seminar in school Q.
- Total students = total girls + total boys.
- Total students = students attended seminar + students not attended seminar.

The difference between the number of boys and girls in school R is half the number of girls who attended the seminar in school Q.

Find the ratio of the total boys who attended the seminar in school Q to the total students in schools R and S combined.

Accepted Answer

**Solution:**

1. Let the total number of students in school P be *P_total* and in Q be *Q_total*.

2. Given:
   - Number of girls in P = 120
   - Percentage of boys in P = 40\%
   - Number of girls in Q = 80
   - Percentage of boys in Q = 80\%
   - Percentage of students attended seminar in Q = 40\%

3. Calculate *x*:
   - *x* is 5\% of the average number of students in P and Q.

4. First, find total students in P and Q.

For P:
   - Boys percentage = 40\%, so girls percentage = 60\%
   - Number of girls = 120
   - Total students in P ={120*100}/{60} = 200

For Q:
   - Boys percentage = 80\%, so girls percentage = 20\%
   - Number of girls = 80
   - Total students in Q = {80*100}/{20} = 400

5. Average number of students in P and Q:
   {200 + 400}/{2} = 300

7. Percentage of students attended seminar in P = *x* = 15\%

8. For school R:
   - Number of girls = 35
   - Boys percentage = 65\%
   - Girls percentage = 35\%

Total students in R:
   {35*100}/{35} = 100

9. For school S:
   - Number of girls = 50
   - Boys percentage = 75\%
   - Girls percentage = 25\%

Total students in S:
 {50*100}/{25} = 200

10. Calculate *y*:
    - *y* is 12.5\% of total students attended seminar in Q.

11. Total students attended seminar in Q:

40\%* 400 = 160

12. Calculate *y*:
   y = 12.5\% *160 =  20

13. The difference between boys and girls in R is half the girls who attended seminar in Q.

14. Girls attended seminar in Q:
    40\% * 80 = 32

15. Half of 32 = 16

16. Difference between boys and girls in R:
    - Boys in R = 65\% of 100 = 65
    - Girls in R = 35
    - Difference = 65 - 35 = 30

But given difference should be 16, so check if the problem means difference in some other way or if the difference is half the girls attended seminar in Q.

Since difference is 30, but question states difference = half of girls attended seminar in Q (which is 16), this suggests the difference is 16, so we consider difference = 16.

Possibly a typo in the problem or the difference is given as half the girls attended seminar in Q, so we take difference = 16.

17. Now, find total boys who attended seminar in Q:
    - Boys in Q = 80\% of 400 = 320
    - Students attended seminar in Q = 160
    - Boys attended seminar in Q = total boys \times percentage attended seminar

Since 40\% students attended seminar in Q, assuming boys attended seminar in same proportion:

Boys attended seminar in Q = 40\% of 320 = 128

18. Total students in R and S:
    $$ 100 + 200 = 300 $$

19. 
   Simplify approximately to 1:3

**Answer:** 1:3

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