Question

Solve this:

Q. The participants of a quiz are divided equally into two groups. In the first group, there are 20 more boys than girls. In the second group, there are 12 more girls than boys. 45% of all the participants are girls.
How many participants are boys?

Answer 1

Dear Student,

$$\begin{gathered} Letthetotalnumberofparticipantsbex. \\ Numberofgirls=\frac{45}{100}\times x=\frac{9x}{20} \\ Numberofboys=\frac{55}{100}\times x=\frac{11x}{20} \\ Then,Infirstgroup\frac{11x}{20}+20=\frac{9x}{20} \\ \frac{11x+400}{20}=\frac{9x}{20} \\ 220x+8000=180x \\ 40x=8000 \\ x=200 \\ So,thenumberofboys=\frac{11}{20}\times 200=110 \end{gathered}$$
Regards