We know that during the years $\(1980-1985,10 \%\)$ of the population of a city migrated to another city whereas the percentage of migrated people from 1980 - 1990 was $\(20 \%\)$; we need to find the percentage of migrated people during the year 1985-1990.

Let the migration percentage from 1985-1990 be $\(\mathrm{x} \%\)$.
When there are two successive changes on a single value say $\(a \%\)$ and then $\(b \%\)$, the net percentage change on the value is of $\(\left(a+b+\frac{a b}{100}\right) \%\)$.

Here the two successive changes of migration from 1980-1985 \& 1985-1990 are of 10\% and $\times \%$ respectively and the net change from $1980-1990$ is given to be $\(20 \%\)$, so we get

$\(\left(-10+(-x)+\frac{(-10) \times(-x)}{100}\right) \%=-20 \% \Rightarrow x\left(-1+\frac{1}{10}\right)=-10 \Rightarrow x=10 \times \frac{-10}{9}=-\frac{100}{9} \%\)$

(Since migration is a decrease negative signs would be taken before the percentages)

Hence the answer is (C).