If a/b = b/c = c/d, then b^3 + c^3 + d^3a^3 + b^3 + c^3 will be equal to -

Answer: Option D

$$\begin{array}{rl}& \text{Let }\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=k\\ & \text{Then,}\\ & a=bk,\\ & b=ck,\\ & c=dk\\ & \text{Also,}\\ & \Rightarrow \frac{a}{b}\times \frac{b}{c}\times \frac{c}{d}=k^3\\ & \Rightarrow k^3=\frac{a}{d}\\ & \therefore \frac{b^3+c^3+d^3}{a^3+b^3+c^3}\\ & =\frac{b^3+c^3+d^3}{{\left(bk\right)}^3+{\left(ck\right)}^3+{\left(dk\right)}^3}\\ & =\frac{b^3+c^3+d^3}{k^3\left(b^3+c^3+d^3\right)}\\ & =\frac{1}{k^3}\\ & =\frac{d}{a}\end{array}$$