If a : b :: b : c, c = 9a and b = 6, then find the positive value of c.

Correct option is B

Given:
a : b :: b : c
c = 9a
b = 6
Solution:
​$$a : b :: b : c\\\Rightarrow \frac{a}{b} = \frac{b}{c}\\\Rightarrow a \cdot c = b^2\\\text{Substitute the given values:}\\a \cdot (9a) = 6^2\\\Rightarrow 9a^2 = 36\\\Rightarrow a^2 = \frac{36}{9} = 4\\\Rightarrow a = 2\\c = 9a = 9 \times 2 = 18\\$$​​