Question

Two numbers $A$ and $B$ are such that the sum of $5\%$ of $A$ and $4\%$ of $B$ is ${\left(\frac{2}{3}\right)}^{rd}$ of the sum of $6\%$ of $A$ and $8\%$ of $B$. Find the ratio $A:B$.

• A. $4:3$
• B. $3:4$
• C. $1:1$
• D. $2:3$

Answer 1

Answer: (A)

$4:3$

Given, $5\%$ of $A+4\%$ of $B=\frac{2}{3}(6\%$ of $A+8\%$ of $B$)
$\Rightarrow \frac{5A}{100}+\frac{4B}{100}=\frac{2}{3}\left(\begin{array}{c}\frac{6A}{100}+\frac{8B}{100}\end{array}\right)$

$\Rightarrow \frac{5A}{100}-\frac{12A}{300}=\frac{16B}{300}-\frac{4B}{100}$

$\Rightarrow \frac{15A-12A}{300}=\frac{16B-12B}{300}$.

$\Rightarrow 3A=4B$

$\Rightarrow \frac{A}{B}=\frac{4}{3}$

$\Rightarrow A:B=4:3$