If \(A:B=\frac{1}{2}:\frac{5}{8}, B:C=\frac{1}{3}:\frac{4}{5}\) and \(C:D=\frac{3}{4}:\frac{5}{16}\), then the ratio \(A: B: C: D\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(4:5:12:5\)
Each ratio of fractions is first turned into whole numbers (multiply both terms by the LCM of the denominators). The ratios are then joined through the common term, which must have the same value in both.
\(\displaystyle A:B=\frac{1}{2}:\frac{5}{8}=4:5\) (both terms \(\times8\))
\(\displaystyle B:C=\frac{1}{3}:\frac{4}{5}=5:12\) (both terms \(\times15\))
\(\displaystyle C:D=\frac{3}{4}:\frac{5}{16}=12:5\) (both terms \(\times16\))
B is 5 in the first two ratios and C is 12 in the last two, so no further scaling is needed: \(A:B:C:D=4:5:12:5\).