Answer:
[tex] \sf \green {\therefore \: 1) \: 200 \: teachers}[/tex]
[tex] \sf \green {2) \: Population \: (before \: 3 \: years)} [/tex] [tex] \sf \green {= 127440}[/tex]
Step-by-step explanation:
1. Percentage of gents teachers = 55%
Percentage of lady teachers = 100% - 55% = 45%
Let the total no. of teachers be 'x'
45% of x = 90 lady teachers
[tex] \sf \frac{ \cancel{45}^{ \: 9} }{ _{20 \: }\cancel{100} } \times x = 90 = \frac{9 \times x}{20 \times 1} = 90[/tex]
[tex] \sf \frac{9x}{20} = 90[/tex]
[tex] \sf 9x = 90 \times 20[/tex]
[tex] \sf 9x = 1800[/tex]
[tex] \sf x = \frac{1800}{9} = 200[/tex]
Total no. of teachers = 2002. Percentage of increase per year = 20%
Percentage of increase in three years = 20% × 3 = 60%
Let the population of a city 3 years before be 'x'
x + 60% of x = 203904
[tex] \sf x + x( \frac{ \cancel{60}^{ \: 3} }{ _{5 \: }\cancel{100}} ) = 203904[/tex]
[tex] \sf x + \frac{3x}{5} = 203904[/tex]
[tex] \sf \frac{5x}{5} + \frac{3x}{5} = 203904[/tex]
[tex] \sf \frac{8x}{5} = 203904[/tex]
[tex] \sf 8x = 203904 \times 5[/tex]
[tex] \sf 8x = 1019520[/tex]
[tex] \sf \frac{ \cancel{1019520}^{ \: \: 127440} }{_{1 \: \: } \cancel{8}} = 127440[/tex]
Before three years, the population was 127440.