In a city, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. What percentage of the total population comprises of females ?

Answer: Option B

Let the total population be x
Then, migrant population :
$$\begin{array}{rl}& =35\%\text{ of }x\\ & =\left(\frac{35}{100}\times x\right)\\ & =\frac{7x}{20}\end{array}$$
Local population :
$$\begin{array}{rl}& =\left(x-\frac{7x}{20}\right)\\ & =\frac{13x}{20}\end{array}$$
Number of rural migrants :
$$\begin{array}{rl}& =20\%\text{ of }\frac{7x}{20}\\ & =\left(\frac{20}{100}\times \frac{7x}{20}\right)\\ & =\frac{7x}{100}\end{array}$$
Number of urban migrants :
$$\begin{array}{rl}& =\left(\frac{7x}{20}-\frac{7x}{100}\right)\\ & =\frac{28x}{100}\\ & =\frac{7x}{25}\end{array}$$
Female population :
$$48\%\text{ of }\frac{13x}{20}+30\%\text{ of }\frac{7x}{100}$$     $$+40\%\text{ of }\frac{7x}{25}$$
$$=\left(\frac{48}{100}\times \frac{13x}{20}\right)+\left(\frac{30}{100}\times \frac{7x}{100}\right)$$      $$+\left(\frac{40}{100}\times \frac{7x}{25}\right)$$
$$\begin{array}{rl}& =\frac{39x}{125}+\frac{21x}{1000}+\frac{14x}{125}\\ & =\frac{445x}{1000}\end{array}$$
∴ Required percentage :
$$\begin{array}{rl}& =\left(\frac{445x}{1000}\times \frac{1}{x}\times 100\right)\%\\ & =44.50\%\end{array}$$