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 $\mathrm{A}: \mathrm{B}$.
(a)2: 3
(b)1: 1
(c)3: 4
(d)4: 3
Answer
Answer (as printed): D
Explanation
5\% of $A+4 \%$ of $B=\frac{2}{3}$ (6\% of $A+8 \%$ of $B$ ) $$\begin{aligned} & \Leftrightarrow \frac{5}{100} A+\frac{4}{100} B=\frac{2}{3}\left(\frac{6}{100} A+\frac{8}{100} B\right) \\ & \Leftrightarrow \frac{1}{20} A+\frac{1}{25} B=\frac{1}{25} A+\frac{4}{75} B \\ & \Leftrightarrow\left(\frac{1}{20}-\frac{1}{25}\right) A=\left(\frac{4}{75}-\frac{1}{25}\right) B \\ & \Leftrightarrow \frac{1}{100} A=\frac{1}{75} B \Leftrightarrow \frac{A}{B}=\frac{100}{75}=\frac{4}{3} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.