The half of the average value of three number is 20. The second number is thrice the third number and first number is twice the second number. What is the sum of smallest and largest number?

Let the three numbers be $$a,b$$ and $$c$$ in decreasing order. 

Half of the average of these 3 numbers is,

$$\dfrac{1}{2}\times\ \dfrac{a\ +\ b\ +\ c}{3}\ =\ 20$$

$$\ a\ +\ b\ +\ c\ =\ 120$$ --(1)

We can see that the first number mentioned is the highest in the question, and its value is given to be,

$$a=2b$$ --(2)

The second number value is given to be,

$$b=3c$$ --(3)

So, the value $$a$$ can also be written as, 

$$a=2b=2*3c=6c$$ --(4)

Substituting (3) and (4) in (1), we get,

$$6c+3c+c=120$$

$$10c=120$$

$$c=12$$

$$a=6c=72$$

Sum of smallest and largest numbers can be calculated as,

$$a+c=72+12=84$$.

Hence, the correct answer is option C.