When x is added to each of 8, 14, 20 and 30, then the numbers, so obtained,in this order form a proportion. What is the mean proportional between $$(x - 2)  and  (7x + 2)$$?

Given,

When x is added to each of 8, 14, 20 and 30, then the numbers, so obtained,in this order form a proportion.

According to Question, 

$$\frac{8+x}{14+x}=\frac{20+x}{30+x}$$

$$240+8x+30x+x^2=280+14x+20x+x^2$$

$$4x=40$$

$$x=10$$

As we know, 

Mean proportion of two numbers a and b = $$\sqrt{\ a\times\ b}$$

we have two numbers :  $$(x - 2) and (7x + 2)$$

i.e; 8 and 72

Mean proportion = $$\sqrt{\ 8\times\ 72}$$

= $$\sqrt{\ 576}=24$$

Hence, Option C is correct.