One - fourth of sixty percent of a number is equal to two - fifths of twenty percent of another number. What is the respective ratio of the first number to the second number ?

Solution(By Examveda Team)

Let the numbers be x and y
$$\eqalign{ & {\text{Then,}} \cr & = \frac{1}{4}{\text{ of }}\left( {60\% {\text{ of }}x} \right) \cr & = \frac{2}{5}{\text{ of }}\left( {20\% {\text{ of }}y} \right) \cr & \Rightarrow \left( {\frac{1}{4} \times \frac{{60}}{{100}} \times x} \right) = \left( {\frac{2}{5} \times \frac{{20}}{{100}} \times y} \right) \cr & \Rightarrow \frac{{3x}}{{20}} = \frac{{2y}}{{25}} \cr & \Rightarrow \frac{x}{y} = \frac{2}{{25}} \times \frac{{20}}{3} = \frac{8}{{15}} \cr & \Rightarrow x:y = 8:15 \cr} $$