Six numbers a, b, c, d, e, f are such that ab = 1, bc = 1/2, cd = 6, de = 2, and ef = 1/2. What is the value of (ad : be : cf)?

Correct option is D

Given:
ab = 1, bc = $$\frac 12$$​, cd = 6, de = 2, and ef =$$\frac 12$$​​
Solution:
​$$a = a\\\ \\\text{From } ab = 1 \Rightarrow b = \frac{1}{a}\\\ \\\text{From } bc = \frac{1}{2} \Rightarrow \frac{1}{a} \cdot c = \frac{1}{2} \Rightarrow c = \frac{1}{2}a\\\ \\\text{From } cd = 6 \Rightarrow \frac{1}{2}a \cdot d = 6 \Rightarrow d = \frac{12}{a}\\\ \\\text{From } de = 2 \Rightarrow \frac{12}{a} \cdot e = 2 \Rightarrow e = \frac{a}{6}\\\\\ \\\text{From } ef = \frac{1}{2} \Rightarrow \frac{a}{6} \cdot f = \frac{1}{2} \Rightarrow f = \frac{3}{a}\\$$ 
$$ad = a \cdot \frac{12}{a} = 12\\\\be = \frac{1}{a} \cdot \frac{a}{6} = \frac{1}{6}\\cf = \frac{1}{2}a \cdot \frac{3}{a} = \frac{3}{2}\\$$ 
To find ad : be : cf: = $$12 \times 6 : \frac{1}{6} \times 6 : \frac{3}{2} \times 6 = 72 : 1 : 9$$​​