If a : (b + c) = 3 : 5 and b : (c + a) = 9 : 11, then c : (a + b) = ?

7 : 33

In these type of questions always note that the total amount/ratio must be same in all conditions.

⇒ A : (B + C) = 3 : 5  = 8(total)

⇒ B : (C + A) = 9 : 11 = 20 (total)

make the total equal,

⇒ A : (B + C) = 15 : 25  = 40 (total)

⇒ B : (A + C) = 18 : 22 = 40 (total)

Therefore,

A = 15, B = 18 & C = 40 -(15 +18) =7

A     :     B     :     C

15    :   18    :     7  = 40  

Here,

⇒ C : (A + B) = 7 : 33