If A : B = 3 : 2 and B : C = 3 : 4, then A : C is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9 : 8
The two ratios share B, so B is first made the same number in both; A and C can then be compared directly.
B is 2 in the first ratio and 3 in the second; the LCM of 2 and 3 is 6
A : B \(=3:2=9:6\)
B : C \(=3:4=6:8\)
So A : B : C \(=9:6:8\), and A : C \(=9:8\)
Shortcut: A : C \(\displaystyle =\frac{A}{B}\times\frac{B}{C}=\frac{3}{2}\times\frac{3}{4}=\frac{9}{8}\), that is, 9 : 8.