Problem: If yz:zx:xy=1:2:3yz: zx: xy=1: 2: 3yz:zx:xy=1:2:3, then xyz:yzx\dfrac{x}{yz}: \dfrac{y}{zx}yzx:zxy is equal to
Answer Choices:
A. 3:23:23:2
B. 1:21:21:2
C. 1:41:41:4
D. 2:12:12:1
E. 4:14:14:1 Solution:
The ratio xyz:yzx=zxyz:zzzx=2:1y=4:1\frac{x}{y z}: \frac{y}{z x}=\frac{z x}{y z}: \frac{z z}{z x}=2: \frac{1}{y}=4: 1yzx:zxy=yzzx:zxzz=2:y1=4:1 because it is given that yz:zx=1:2y z: z x=1: 2yz:zx=1:2 and bence 2yz=zx2 y z=z x2yz=zx so that zxyz=2\frac{zx}{yz}=2yzzx=2 and yzzx=12\frac{yz}{zx}=\frac{1}{2}zxyz=21.