Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.
8 : 32 :: 12 : 72 :: 18 : ?

8 : 32

Second number = $$\frac{\left(first\ number\right)^2}{2}$$

= $$\frac{\left(8\right)^2}{2}$$

= $$\frac{64}{2}$$

= 32

12 : 72

Second number = $$\frac{\left(first\ number\right)^2}{2}$$

= $$\frac{\left(12\right)^2}{2}$$

= $$\frac{144}{2}$$

= 72

18 : ?

Second number = $$\frac{\left(first\ number\right)^2}{2}$$

= $$\frac{\left(18\right)^2}{2}$$

= $$\frac{324}{2}$$

= 162

Hence 162 will come in place of the question mark.