Question 1032126
Regarding the children (boys and girls),
the number of boys is exactly {{{110/100=11/10}}} the number of girls,
and the number of boys and the number of girls should be whole numbers.
So, {{{g}}}= number of girls, and
{{{(11/10)g}}}= number of boys,
must both be whole numbers.
So would be {{{g+(11/10)g=(21/10)g}}}= number of children.
 
The ratio of children to adults is {{{120/100=6/5}}} ,
so the ratio of adults to children is {{{5/6}}} ,
and the total number of adults is
{{{(5/6)(21/10)g=(7/4)g}}} .
 
Among the adults (men and women),
the ratio of number of men to total number of adults is
{{{100/(100+115)=100/215=20/43}}} , and
the ratio of number of women to total number of adults is
{{{115/(100+115)=115/215=23/43}}} .
So,
the number of men is {{{(20/43)(7/4)g=(35/43)g}}} , and
the number of women is {{{(23/43)(7/4)g=(23*7/(4*43))g}}} .
 
The number of women, men, and boys, respectively, are
{{{(23*7/(4*43))g}}} , {{{(35/43)g}}} , and {{{(11/10)g}}} ,
and they must all be whole numbers,
which means that {{{g}}} must be a multiple of
{{{4*43}}} , {{{43}}} , and {{{10}}} .
The least common multiple is
{{{5*4*43=20*43=highlight(860)}}} .
 
The total population would be
{{{g+(23*7/(4*43))g+(35/43)g+(11/10)g=((860+5*23*7+20*35+86*11)/860)g=((860+805+700+946)/860)g=(3311/860)g}}} .

With {{{g=860}}} , the total population would be {{{3311}}} .
The next multiple of {{{860}}} , {{{2*860}}} ,
would make the total population {{{2*3311=6622>6000}}} .
 
So, the number of girls is {{{g=highlight(860)}}} .
The number of boys is {{{(11/10)g=(11/10)860=highlight(946)}}} .
The number of men is {{{(35/43)g=(35/43)860=highlight(700)}}} .
The number of women is {{{(23*7/(4*43))g=(23*7/(4*43))860=highlight(805)}}} .

NOTE:
There is often more than one way to solve a problem.
In real life, the problem solver should choose
a way that is short and comfortable for him/her.
In school, we also need to cater to the teacher's preferences.