​If a : b :: b : c; c = 4a; and b = 6, find the positive value of c

Correct option is B

Given :

a : b : : b : c 

c = 4a , b = 6

Solution :

$$\frac{a}{b}=\frac{b}{c}$$

  $$a\times c= b^2$$ 

Now,  by value of c and b 

 $$4a^2=6^2$$

 $$a^2=\frac{36}{4}$$

 $$a^2= 9 \\ \ \\ a= 3$$

Now, for c,

c = 4$$a$$​   

c = 4$$\times$$ 3 = 12 .

The correct answer is option (b) 12 .