If a3 = 117 + b3 and a = 3 + b, then the value of a + b is?

Answer: Option A

$$\begin{array}{rl}& a^3=117+b^3\text{ , }a=3+b\\ & a^3-b^3\text{ = 117}......\text{(i)}\\ & a-b=3........(ii)\\ & \text{Put }a=5,b=2\\ & \text{Both equation satisfy}\\ & \text{Now, }a+b=5+2=7\end{array}$$