The population of a district is 369000,

$ \text{Total population} = 369000 $
$ \text{Number of males} = 186000 $
$ \text{Number of females} = 369000 - 186000 = 183000 $
$ \text{Total literates} = 45% \text{ of } 369000 = 0.45 \times 369000 = 166050 $
$ \text{Literate males} = 45% \text{ of } 186000 = 0.45 \times 186000 = 83700 $
$ \text{Literate females} = 166050 - 83700 = 82350 $
$ \text{Percentage of literate females} = \frac{82350}{183000} \times 100 \approx 45% $
45%