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 percent of the total population comprises of females?
(a)42.75\%
(b)44.5\%
(c)48\%
(d)None of these
Answer
Answer (as printed): B
Explanation
Let the total population be $x$. Then, migrant population $=35 \%$ of $x=\left(\frac{35}{100} \times x\right)=\frac{7 x}{20}$. $$\text { Local population }=\left(x-\frac{7 x}{20}\right)=\frac{13 x}{20} \text {. } \text { Number of rural migrants }=20 \% \text { of } \frac{7 x}{20}=\left(\frac{20}{100} \times \frac{7 x}{20}\right)=\frac{7 x}{100} \text {. }$$ Number of urban migrants $=\left(\frac{7 x}{20}-\frac{7 x}{100}\right)=\frac{28 x}{100}=\frac{7 x}{25}$. Female population $=48 \%$ of $\frac{13 x}{20}+30 \%$ of $\frac{7 x}{100}+40 \%$ of $\frac{7 x}{25}$ $$\begin{aligned} & =\left(\frac{48}{100} \times \frac{13 x}{20}\right)+\left(\frac{30}{100} \times \frac{7 x}{100}\right)+\left(\frac{40}{100} \times \frac{7 x}{25}\right) \\ & =\frac{39 x}{125}+\frac{21 x}{1000}+\frac{14 x}{125}=\frac{445 x}{1000} . \end{aligned}$$ ∴ $\quad$ Required percentage $=\left(\frac{445 x}{1000} \times \frac{1}{x} \times 100\right) \%=44.5 \%$.
Explanation as extracted from the printed page; notation may be imperfect.