Comparing Percentages without calculating

Question

Consider the following imaginary scenario There are two groups X and Y containing six categories A,B,C,D,E and F which represent ethnic groups

X(150million=Total Population in Year 2000)           Y(210million Total Poptulation in Year 2020)
A=12%                                                  A=12%
B=21%                                                  B=17%
C=15%                                                  C=13.33%
D=19%                                                  D=14.44%
E=43%                                                  E=38%
F=15%                                                  F=13.9%

Although by calculating each percentage for the two groups for each categories I can check which categories have actual increase but is there a trick like some threshold percentage on actual value that I could use to check which categories have increased or decreased? for example for category A in Y if that were above 12 then I was perfect sure that category A in Y has increased since Total of Y is greater than X and so does percentage.

Answer 1

Since $Y=210$, $X=150$, $(Y-X)/X=60/150$, so $Y=X+60/150X=(1+60/150)X=1.4X$. So if 1.4 times the percentage in $Y$ is greater than the percentage in $X$, then it increased.

For example, for category B, you want to compare $17\%Y$ and $21\%X$. Since $Y=1.4X$, we actually want to compare $17\%\cdot 1.4 X$ and $21\%X$, which is to compare $1.4\cdot 17\%$ and $21\%$. If $1.4\cdot 17$ is greater than $21$, than B increased.