If (x3 - y3) : (x2 + xy + y2) = 5 : 1 and (x2 - y2) : (x - y) = 7 : 1, then the ratio 2x : 3y equals = ?

Answer: Option D

According to question,
$$\begin{array}{rl}& \frac{x^3-y^3}{x^2+xy+y^2}=\frac{5}{1}\\ & \frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{x^2+xy+y^2}=\frac{5}{1}\\ & x-y=\mathrm{5.....}(\text{i})\\ & \frac{x^2-y^2}{x-y}=\frac{7}{1}\\ & \frac{\left(x+y\right)\left(x-y\right)}{x-y}=\frac{7}{1}\\ & x+y=\mathrm{7.....}(\text{ii})\\ & \text{Solve equations (i) and (ii)}\\ & x=6\\ & y=1\\ & \therefore \frac{2x}{3y}=\frac{2\times 6}{3\times 1}\\ & =\frac{12}{3}\\ & =\frac{4}{1}\\ & =4:1\end{array}$$