Solution
A : B = 3 : 4 Eq.(i)
B : C = 2 : 3 Eq.(ii)
Merge Eq.(i) and Eq.(ii) by multiplying 1 and 2 respectively.
A : B : C = 3 : 4 : 6
Let's assume A = 3y, B = 4y and C = 6y.
the value of $$A + B : B + C : C + A$$ is = (A + B) : (B + C) : (C + A)
= (3y+4y) : (4y+6y) : (6y+3y)
= 7y : 10y : 9y
= 7 : 10 : 9
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