Read the information and answer the following question.
The total number of people in organization B is 500. In organization A, the total number of students equals the number of male teachers. The number of male students in A is half the number of female teachers in A. The sum of male students and female teachers in A equals the number of male students in B. The number of male and female teachers in B are equal, and each is 25 more than the number of female students in B. The female teachers in B number 75, and the total number of females in both organizations is 350.
What is the difference between the total number of people in both organizations?

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**Solution:**
![image.png](https://res.cloudinary.com/aptidude/image/upload/v1755955284/aptidude_questions/htwtiftptg4miiexlpgt.png)

1. Given total people in organization B = 500.

2. Female teachers in B = 75 (given).

3. Male teachers in B = Female teachers in B = 75 (since they are equal).

4. Female students in B = Male teachers in B - 25 = 75 - 25 = 50.

5. Male students in B = Total in B - (Male teachers + Female teachers + Female students) = 500 - (75 + 75 + 50) = 500 - 200 = 300.

6. Let the number of female teachers in A be *x*.

7. Male students in A = Half of female teachers in A = $\frac{x}{2}$.

8. Total students in A = Male students + Female students = Male teachers in A (given).

9. Sum of male students and female teachers in A = Male students in B = 300.

So, $\frac{x}{2} + x = 300 \Rightarrow \frac{3x}{2} = 300 \Rightarrow x = 200$.

10. Female teachers in A = 200.

11. Male students in A = $\frac{200}{2} = 100$.

12. Total students in A = Male teachers in A (given). Let male teachers in A be *y*.

13. Total students in A = Male students + Female students = $100 +$ Female students.

14. Since total students in A = Male teachers in A, we have:

$100 +$ Female students = $y$.

15. Total females in both organizations = 350.

Females in A = Female students + Female teachers = $f + 200$.

Females in B = Female students + Female teachers = $50 + 75 = 125$.

So, $f + 200 + 125 = 350 \Rightarrow f + 325 = 350 \Rightarrow f = 25$.

16. Female students in A = 25.

17. Total students in A = $100 + 25 = 125$.

18. Male teachers in A = 125 (from step 14).

19. Total people in A = Male students + Female students + Male teachers + Female teachers = $100 + 25 + 125 + 200 = 450$.

20. Total people in B = 500 (given).

21. Difference between total people in both organizations = $500 - 450 = 50$.

**Answer:** 50

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