Two numbers A and B are such that the sum of 5% of A and 4% of B is two-thirds of the sum of 6% of A and 8% of B. Find the ratio of A : B ?

Answer: Option D

5% of A + 4% of B = $$\frac{2}{3}$$ (6% of A + 8% of B)
$$\iff \frac{5}{100}A+\frac{4}{100}B=$$     $$\frac{2}{3}\left(\frac{6}{100}A+\frac{8}{100}B\right)$$
$$\begin{array}{rl}& \iff \frac{1}{20}A+\frac{1}{25}B=\frac{1}{25}A+\frac{4}{75}B\\ & \iff \left(\frac{1}{20}-\frac{1}{25}\right)A=\left(\frac{4}{75}-\frac{1}{25}\right)B\\ & \iff \frac{1}{100}A=\frac{1}{75}B\\ & \iff \frac{A}{B}=\frac{100}{75}\\ & \iff \frac{A}{B}=\frac{4}{3}\end{array}$$
∴ A : B = 4 : 3