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.

Solution (By Examveda Team)

$$\eqalign{ & 5\% \,{\text{of}}\,A + 4\% \,{\text{of}}\,B = \frac{2}{3}\left( {6\% \,{\text{of}}\,A + \,8\,{\text{of}}\,B} \right) \cr & \Rightarrow \frac{5}{{100}}A + \frac{4}{{100}}B = \frac{2}{3}\left( {\frac{6}{{100}}A + \frac{8}{{100}}B} \right) \cr & \Rightarrow \frac{1}{{20}}A + \frac{1}{{25}}B = \frac{1}{{25}}A + \frac{4}{{75}}B \cr & \Rightarrow \left( {\frac{1}{{20}} - \frac{1}{{25}}} \right)A = \left( {\frac{4}{{75}} - \frac{1}{{25}}} \right)B \cr & \Rightarrow \frac{1}{{100}}A = \frac{1}{{75}}B \cr & \frac{A}{B} = \frac{{100}}{{75}} = \frac{4}{3} \cr & \therefore {\text{Required}}\,{\text{ratio}} = 4:3 \cr} $$