Let us solve this question by assuming values $(\multiples \of 100)$ and not variables $(x)$
Since we know that the female population was twice the male population in 1990, let us assume their respective values as $200$ and $100$
Note that while assuming numbers, some of the population values might come out as a fraction(which is not possible, since the population needs to be a natural number). However, this would not affect our answer, since the calculations are in ratios and percentages and not real values of the population in any given year. Now, we know that the female population became 1.25 times itself in 1990 from what it was in 1980.
Hence, the female population in 1980 $={200/1.25} = 160 $
Also, the female population became $1.2 \times$ itself in 1980 from what it was in 1970.
Hence, the female population in 1970 $= 160/1.2 = 1600/12 = 400/3$
Let the male population in 1970 be $x$. Hence, the male population in 1980 is $1.4x$.
Now, the total population in 1980 $= 1.25 \times$ the total population in 1970.
Hence, $1.25 (x + 400/3) = 1.4x + 160 $
Hence, $x = 400/9$
Population change $= 300 -400/9- 400/3 = 300 - 600/9 =1100/9$
Percentage change =${1100/9}/ {1600/9} × 100 = 1100/ 16 % = 68.75%$