Ratio question

Stumped?

Question: Class A and Class B have the same number of pupils. The ratio of boys in Class A to the number of boys in Class B is 3:2. The ratio of the number of girls in Class A to the number of girls in Class B is 3:5. Find the ratio of the number of boys to the number of girls in Class A.


For those who know Algebra, this can be solved, albeit in a convulated way, by expressing Class A and Class B in terms of the other, i.e.

Class A = Boys(A) + Girls(A) or C(A) = B(A)+G(A)

Given:
B(A):B(B)=3:2 and G(A):G(B)=3:5

C(A) = 3/2 B(B) + 3/5 G(B)
C(B) = 2/3 B(A) + 5/3 G(A)

Since total in class A and B are equal,
equate the 2.

but there must be an easier method!!!

Try using units method:

Boys(A):Boys(B) = 3:2
Girls(A):Girls(B) = 3:5

Since Class A = Class B in size, Boys(A) + Girls (A) = Boys (B) + Girls (B)

Boys(A):Boys(B) = 3:2 or 6:4 (double)
Girls(A):Girls(B) = 3:5 ..... 3:5

Now units of Class A = units of Class B (9 units)

Now Boys (A) : Girls (A) = 6:3 or 2:1