In a company with a total of 3540 employees, there are 4 departments: Management, HR, Production, and Accounts. The number of females in the HR department is 87.5\% of the number of males in the same department. The number of males in the Production department is 800, which is 25\% more than the number of males in the Management department. The number of females in the Management department is equal to the number of males in the Accounts department. The number of females in the Accounts department is 150 less than the number of males in the same department and 150 more than the number of females in the Production department. The ratio of total employees in the Production department to those in the Accounts department is 19:15.

What percentage more or less is the total number of employees in the HR department compared to the Accounts department?

Question

In a company with a total of 3540 employees, there are 4 departments: Management, HR, Production, and Accounts. The number of females in the HR department is 87.5\% of the number of males in the same department. The number of males in the Production department is 800, which is 25\% more than the number of males in the Management department. The number of females in the Management department is equal to the number of males in the Accounts department. The number of females in the Accounts department is 150 less than the number of males in the same department and 150 more than the number of females in the Production department. The ratio of total employees in the Production department to those in the Accounts department is 19:15.

What percentage more or less is the total number of employees in the HR department compared to the Accounts department?

Accepted Answer

**Solution:**

1. Let the number of males in Management be $ M_m $.

2. Males in Production = 800, which is 25\% more than males in Management:
   $$
 $  800 = M_m + 0.25 M_m = 1.25 M_m \implies M_m = \frac{800}{1.25} = 640$
   $$

3. Females in Management = males in Accounts. Let males in Accounts be $ A_m $, so females in Management = $ A_m $.

4. Females in Accounts = males in Accounts - 150 = $ $A_m - 150 $$.

5. Females in Accounts are 150 more than females in Production:
   $$
 $  A_m - 150 = F_p + 150 \implies F_p = A_m - 300$
   $$

6. Total employees in Production and Accounts are in ratio 19:15.

Total in Production = males in Production + females in Production = $ $800 + F_p = 800 + (A_m - 300) = A_m + 500 $$

Total in Accounts = males in Accounts + females in Accounts = $ $A_m + (A_m - 150) = 2 A_m - 150$ $

Given ratio:
   $$
  $ \frac{A_m + 500}{2 A_m - 150} = \frac{19}{15} $
   $$

7. Cross-multiplied:
   $$
  $ 15 (A_m + 500) = 19 (2 A_m - 150) \ 
   15 A_m + 7500 = 38 A_m - 2850 \ 
   7500 + 2850 = 38 A_m - 15 A_m \ 
   10350 = 23 A_m \ 
   A_m = \frac{10350}{23} = 450 $
   $$

8. Now, females in Management = males in Accounts = 450.

9. Females in Accounts = $ 450 - 150 = 300 $.

10. Females in Production = $ 450 - 300 = 150 $.

11. Total employees in Production = $ 800 + 150 = 950 $.

12. Total employees in Accounts = $ 450 + 300 = 750 $.

13. Females in HR are 87.5\% of males in HR. Let males in HR be $$ H_m $$, females in HR be $ $H_f = 0.875 H_m $$.

14. Total employees in HR = $ $H_m + 0.875 H_m = 1.875 H_m$ $.

15. Total employees in Management = males + females = $ 640 + 450 = 1090 $.

16. Sum of all employees:
    $$
    $1090 + 950 + 750 + 1.875 H_m = 3540 \ 
    2790 + 1.875 H_m = 3540 \ 
    1.875 H_m = 3540 - 2790 = 750 \ 
    H_m = \frac{750}{1.875} = 400 $
    $$

17. Total employees in HR = $ 1.875 \times 400 = 750 $.

18. Total employees in Accounts = 750.

19. Percentage difference between HR and Accounts:
    $$
  $  \frac{750 - 750}{750} \times 100 = 0\% $
    $$

**Answer:** 0\%

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