Question 105881
Originally in the group, 
1.{{{B/(B+G)=60/100}}}
where B-boys and G-girls.
Then the percentage changed to 
2.{{{(B+6)/((B+6)+(G-6))=75/100}}}
Our two equations are then, 
1.{{{B/(B+G)=60/100}}}
2.{{{(B+6)/(B+G)=75/100}}}
Re-writing both equations, you get,
1.{{{B+G=100B/60}}}
2.{{{B+G=100(B+6)/75}}} or
{{{100B/60=100(B+6)/75}}}
{{{75B=60(B+6)}}}
{{{75B=60B+360)}}}
{{{15B=360}}}
{{{B=24}}}
From 1,
1.{{{B+G=100B/60}}}
{{{24+G=100(24)/60}}}
{{{24+G=100(24)/60}}}
{{{24+G=40}}}
{{{G=16}}}
Check your answer.
Originally there were 24 boys and 16 girls and the ratio of boys to girls was 60%. 
{{{24/(24+16)=60/100}}}
{{{24/40=0.6}}}
{{{0.6=0.6}}}
Good answer.
Then 6 more boys, 6 less girls and the ratio of boys to girls was 75%.
{{{(24+6)/(24+6+16-6)=75/100}}}
{{{30/40=0.75}}}
{{{0.75=0.75}}}
Good answer. 
Final answer : 24 boys, 16 girls.