Given that W : X = 5 : 6, X : Y = 3 : 7, and Y : Z = 8 : 9, find the compound ratio W : X : Y : Z.
A. 20 : 24 : 56 : 63 (Correct answer)
B. 5 : 6 : 7 : 9
C. 5 : 6 : 14 : 9
D. 20 : 24 : 42 : 63
Correct Answer
Option A — 20 : 24 : 56 : 63
Detailed Solution & Explanation
The correct answer is 20 : 24 : 56 : 63.
Key Points
Chain the ratios so shared terms match.
W:X = 5:6, X:Y = 3:7, Y:Z = 8:9. Multiply through to a common four-part ratio: W:X:Y:Z = (5·3·8) : (6·3·8) : (6·7·8) : (6·7·9) = 120:144:336:378, which reduces (÷6) to 20:24:56:63.
The technique for ratio chains: scale each pair so the linking term (X, then Y) carries the same value across ratios, then read off all four parts together.