If 3x+y = 81 and 81x-y = 3, then the value of x/y is = ?

Answer: Option D

$$\begin{array}{rl}& \text{According to question,}\\ & \Rightarrow {\text{3}}^{x+y}\text{ = 81}\text{and}\text{8}{\text{1}}^{x-y}\text{ = 3}\\ & \Rightarrow {\text{3}}^{x+y}\text{ = (3}{\text{)}}^4\text{and}{{\left(3\right)}^{4(}}^{x-y)}\text{ = }{\text{3}}^1\\ & \Rightarrow x+y=4\text{and}x-y=\frac{1}{4}\\ & x+y=\mathrm{4......}\text{(i)}\\ & x-y=\frac{1}{4}.....(ii)\\ & \text{Solve the equation of (i) and (ii)}\\ & x=\frac{17}{8},\\ & y=\frac{15}{8},\\ & \Rightarrow \frac{x}{y}=\frac{17}{15}\end{array}$$