Question

30,000 students appeared in a contest. Of them 40% were girls and the remaining boys. If 10% boys and 12% girls won the contest with prizes, find the percentage of students who won prizes.

Answer 1

First, calculate the actual number of boys and girls who were in the contest.  If 40% are girls then 60% were boys, so find 40% of 30,000 and 60% of 30,000.  Remember that in almost all cases, "of" in a word problem means multiplication, and percent always means divide by 100, so "40% of 30,000" translates directly to 40/100 x 30,000.  You can use this in all problems where you see a phrase like "some percent of another."  

Answer 2

I would like to continue the above answer -
Once you get those, you can do the same thing with the results of this calculation and the 10% and 12%, and get the number of boy winners and girl winners.  You can add that to get the total number of winners.   Then divide that by the original number of contestants (30,000) to get the fraction who were winners (a decimal in your calculator) and then convert that back to a percent.