a) 20

b) 25

c) 35

d) 30

correct answer is: d) 30

Explanation

Here,
In a school, the number of students is 660.
And, the ratio of the number of boys and girls was 13\;:\;9\;.
Let,
Number of boys is 13x.
Number of girls is 9x.
According to the question,
\left(13x+9x\right)=660.
\rightarrow 22x=660
\rightarrow x=\large\frac{660}{22} _{[cross multiply]}
\rightarrow x=30
So that,
Number of boys is 13x or \left(13\times30\right)=390.
Number of girls is 9x or \left(9\times30\right)=270.

Now, After a few days 30 girls joined the school but a few boys left. As a result, the ratio of the boys and girls became 6\;:\;5\;.
Let, ‘y’ number of boys left.
So,
390-y\;:\;270+30=\;6\;:\;5
\rightarrow\large\frac{390-y}{270+30}=\frac{6}{5}
\rightarrow5\times\left(390-y\right)=6\times\left(270+30\right) _{[cross multiply]}
\rightarrow 1950-5y=1620+180
\rightarrow 1950-5y=1800
\rightarrow -5y=1800-1950 _{[interchange]}
\rightarrow -5y=-150
\rightarrow y=\large\frac{150}{5}
\rightarrow y=30
\therefore 30 boys left the school.
Ans: The number of boys left the school is 30.

You can phrase this math question in various forms: