If x + y = 15, then the value of (x - 10)3 + (y - 5)3 is?

Answer: Option D

$$\begin{array}{rl}& x+y=15\\ & \Rightarrow x-10=5-y\\ & \Rightarrow x-10=-\left(y-5\right)\\ & \text{Take cube on both sides}\\ & \Rightarrow {\left(x-10\right)}^3=-{\left(y-5\right)}^3\\ & \Rightarrow {\left(x-10\right)}^3+{\left(y-5\right)}^3=0\end{array}$$