If a/b = 4/5 and b/c = 1516 , then 18c^2 - 7a^245c^2 + 20a^2 is equal to?

Answer: Option D

$$\begin{array}{rl}& \frac{a}{b}\text{ = }\frac{4}{5}\text{ and }\frac{b}{c}\text{ = }\frac{15}{16}\\ & \Rightarrow \frac{a}{b}\times \frac{b}{c}\text{ = }\frac{4}{5}\times \frac{15}{16}\\ & \Rightarrow \frac{a}{c}=\frac{3}{4}\\ & \therefore \frac{18c^2-7a^2}{45c^2+20a^2}\\ & =\frac{c^2\left(18-7\frac{a^2}{c^2}\right)}{c^2\left(45+20\frac{a^2}{c^2}\right)}\\ & =\frac{18-7{\left(\frac{a}{c}\right)}^2}{45+20{\left(\frac{a}{c}\right)}^2}\\ & =\frac{18-7\times \frac{9}{16}}{45+20\times \frac{9}{16}}\\ & =\frac{18-\frac{63}{16}}{45+\frac{45}{4}}\\ & =\frac{225\times 4}{16\times 225}\\ & =\frac{1}{4}\end{array}$$