Select the option in which the numbers are related in the same way as are the numbers in the given set.
(4, 67, 20)

The logic here is

$$4^3+3=64+3=67$$ $$\longrightarrow\ $$ $$\text{first number}^3+3=\ \text{second number}$$

$$4\times\left(4+1\right)=4\times5=20$$ $$\longrightarrow\ $$ $$\text{first number}\times\left(\text{first number}+1\right)=\text{third number}$$

Similarly,

$$3^3+3=27+3=30$$ $$\longrightarrow\ $$ $$\text{first number}^3+3=\ \text{second number}$$

$$3\times\left(3+1\right)=3\times4=12$$ $$\longrightarrow\ $$ $$\text{first number}\times\left(\text{first number}+1\right)=\text{third number}$$

$$\therefore\ $$(3, 30, 12) are related in the same way (4, 67, 20) are related.

Hence, the correct answer is Option C