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 8% of B. Find the ratio of A: B.

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

Answer 1

The correct option is D 4 : 3

$5\%ofA+4\%ofB=\frac{2}{3}(6\%ofA+8\%ofB)$
$\Rightarrow \frac{5}{100}A+\frac{4}{100}B=\frac{2}{3}(\frac{6}{100}A+\frac{8}{100}B)$
$\Rightarrow \frac{1}{20}A+\frac{1}{25}B=\frac{1}{25}A+\frac{4}{75}B$
$\Rightarrow (\frac{1}{20}-\frac{1}{25})A=(\frac{4}{75}-\frac{1}{25})B$
$\Rightarrow \frac{1}{100}A=\frac{1}{75}B$
$\frac{A}{B}=\frac{100}{75}=\frac{4}{3}$
$\therefore$ Required ratio=4:3.