General Solution:
From the table:
Public sector employees in Building A = 120
Public sector employees in Building B = a
Public sector employees in Building C = 90
Public sector employees in Building D = 2a
Total public sector employees =120 + a + 90 + 2a = 300
210 + 3a = 300
3a = 90
a = 30
Building A:
Public sector employees = 120
Ratio of public to private = 3 : 2
Private sector employees = 2/3 × 120 = 80
Vacant flats = 20% of total flats
Let total flats = F
Vacant flats = 0.20F
Total flats = Public + Private + Vacant
120 + 80 + 0.20F = F
200 = 0.80F
F = 250
Total flats in Building A = 250
Building B:
Public sector employees =a = 30
Ratio of public to private = 3 : 5
Private sector employees = 5/3 × 30 = 50
Vacant flats = 20% of total flats
Let total flats = F
Vacant flats = 0.20F
Total flats = Public + Private + Vacant
30 + 50 + 0.20F = F
80 = 0.80F
F = 100
Total flats in Building B = 100
Building C:
Public sector employees = 90
Ratio of public to private = 2 : 3
Private sector employees = 3/2 × 90 = 135
Vacant flats = 25% of total flats
Let total flats = F
Vacant flats = 0.25F
Total flats = Public + Private + Vacant
90 + 135 + 0.25F = F
225 = 0.75F
F = 300
Total flats in Building C = 300
Building D:
Public sector employees = 2a = 60
Ratio of public to private = 5 : 4
Private sector employees = 4/5 × 60 = 48
Vacant flats = 55% of total flats
Let total flats = F
Vacant flats = 0.55F
Total flats = Public + Private + Vacant
60 + 48 + 0.55F = F
108 = 0.45F
F = 240
Total flats in Building D = 240
Thus,
| Building | Public Sector Employees | Private Sector Employees | Vacant Flats | Total Flats |
|---|
| A | 120 | 80 | 50 | 250 |
| B | 30 | 50 | 20 | 100 |
| C | 90 | 135 | 75 | 300 |
| D | 60 | 48 | 132 | 240 |
Calculations:
Total public sector employees in Building A = 120
Ratio of male to female employees in Building A = 5 : 3
Let the number of male employees = 5x
Let the number of female employees = 3x
Total employees = 5x + 3x = 8x
8x = 120
x = 15
Male employees in Building A = 5x = 5 × 15 = 75
Female employees in Building A = 3x = 3 × 15 = 45
Total public sector employees in Building C = 90
Ratio of male to female employees in Building C = 4 : 5
Let the number of male employees = 4y
Let the number of female employees = 5y
Total employees =4y + 5y = 9y
9y = 90
y = 10
Male employees in Building C = 4y = 4 × 10 = 40
Female employees in Building C = 5y = 5 × 10 = 50
Total public sector employees in Building A = 120
Total public sector employees in Building C = 90
Total employees in A and C = 120 + 90 = 210
Female employees in Building A = 45
Female employees in Building C = 50
Total female employees = 45 + 50 = 95
Percentage of female employees = (Total female employees / Total employees in A and C) × 100
Percentage = 95 / 210 × 100 = 45.24%
Thus, the percentage of female public sector employees in Buildings A and C together is 45.24%.