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 A : B ?

Solution(By Examveda Team)

5% of A + 4% of B = $$\frac{2}{3}$$ (6% of A + 8% of B)
$$ \Leftrightarrow \frac{5}{{100}}A + \frac{4}{{100}}B = $$     $$\frac{2}{3}\left( {\frac{6}{{100}}A + \frac{8}{{100}}B} \right)$$
$$\eqalign{ & \Leftrightarrow \frac{1}{{20}}A + \frac{1}{{25}}B = \frac{1}{{25}}A + \frac{4}{{75}}B \cr & \Leftrightarrow \left( {\frac{1}{{20}} - \frac{1}{{25}}} \right)A = \left( {\frac{4}{{75}} - \frac{1}{{25}}} \right)B \cr & \Leftrightarrow \frac{1}{{100}}A = \frac{1}{{75}}B \cr & \Leftrightarrow \frac{A}{B} = \frac{{100}}{{75}} \cr & \Leftrightarrow \frac{A}{B} = \frac{4}{3} \cr} $$
∴ A : B = 4 : 3