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

The correct option is A $4:3$

Given that $5\%\text{of}A+4\%\text{of}B=\frac{2}{3}(6\%\text{of}A+8\%\text{of}B)$

$\Rightarrow$ $\frac{5}{100}A+\frac{4}{100}B=\frac{2}{3}(\frac{6}{100}A+\frac{8}{100}B)$

$\Rightarrow$ $\frac{1}{20}A+\frac{1}{25}B=\frac{1}{25}A+\frac{4}{75}B$

$\Rightarrow$ $(\frac{1}{20}-\frac{1}{25})A=(\frac{4}{75}-\frac{1}{25})B$

$\Rightarrow$ $\frac{1}{100}A=\frac{1}{75}B$

$\Rightarrow$ $\frac{A}{B}=\frac{100}{75}=\frac{4}{3}$

Ths required ratio is $4:3$.