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
2a+5b
3a+6b
=
7
9
Hence
a
b
=1 a>b.....(i) The ratio of boys to girls when B and C are taken together is 3 : 2. Therefore,
5b+8c
6b+5c
=
3
2
b
c
=
1
8
⇒8b=c.......(ii) From Eqs. (i) and (ii), we get a = b and 8a = c Total students in A=2a+3a=5a Total students in B=5b+6b=11b Total students in C=8c+5c=13c Total students in all the classes = 5a+11b+13c=120a Hence, the total number of students is some multiple of 120. 360 is the correct answer among the answer among the answer choices.