Question

Two numbers $A$ and $B$ are such that the sum of $5$% of $A$ and $4$% of $B$ is two-third of the sum of $6$$of$A$and$8B$.Findtherationof$A:B$.

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

Answer 1

Answer: (D)

$4:3$

$5$% of $A+4$% of $B=\frac{2}{3}(6$%of $A+8$% of $B)$
$\Rightarrow$ $\frac{5}{100}A+\frac{4}{100}B=\frac{2}{3}$
$\Rightarrow \frac{1}{20}A+\frac{1}{25}B=\frac{1}{75}A+\frac{4}{75}B$
$\Rightarrow (\frac{1}{20}-\frac{1}{25})A=(\frac{1}{75}-\frac{4}{75})B$
$\Rightarrow \frac{1}{100}A=\frac{1}{75}B$
$\frac{A}{B}=\frac{100}{75}=\frac{4}{3}$