Mathematics
If A : B = 2 : 5 and A : C = 3 : 4, find :
A : B : C.
Ratio Proportion
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Answer
To compare 3 ratios, the consequent of the first ratio and the antecedent of the 2nd ratio must be made equal.
Given that A : B = 2 : 5 and A : C = 3 : 4
Interchanging the first ratio, we have,
B : A = 5 : 2 and A : C = 3 : 4
L.C.M. of 2 and 3 is 6.
⇒ B : A = 5 × 3 : 2 × 3 and A : C = 3 × 2 : 4 × 2
⇒ B : A = 15 : 6 and A : C = 6 : 8
⇒ B : A : C = 15 : 6 : 8
⇒ A : B : C = 6 : 15 : 8.
Hence, A : B : C = 6 : 15 : 8.
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