CAT 2017 Quantitative Ability

Let us try to represent the data in the question
The ratio of boys to girls when Classes A and B are taken together is 7 : 9.
Therefore $\frac{2\mathit{a}+5\mathit{b}}{3\mathit{a}+6\mathit{b}}=\frac{7}{9}$
Hence $\frac{\mathit{a}}{\mathit{b}}=1$
$\mathit{a}>\mathit{b}.....\left(\mathit{i}\right)$
The ratio of boys to girls when B and C are taken together is 3 : 2.
Therefore, $\frac{5\mathit{b}+8\mathit{c}}{6\mathit{b}+5\mathit{c}}=\frac{3}{2}$
$\frac{\mathit{b}}{\mathit{c}}=\frac{1}{8}\Rightarrow 8\mathit{b}=\mathit{c}.......\left(\mathit{i}\mathit{i}\right)$
From Eqs. (i) and (ii), we get a = b and 8a = c
Total students in $\mathit{A}=2\mathit{a}+3\mathit{a}=5\mathit{a}$
Total students in $\mathit{B}=5\mathit{b}+6\mathit{b}=11\mathit{b}$
Total students in $\mathit{C}=8\mathit{c}+5\mathit{c}=13\mathit{c}$
Total students in all the classes = $5\mathit{a}+11\mathit{b}+13\mathit{c}=120\mathit{a}$
Hence, the total number of students is some multiple of 120.
360 is the correct answer among the answer among the answer choices.