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 ?

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  1. 4 : 7
  2. 5 : 9
  3. 8 : 13
  4. Cannot be determine
  5. None of these

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Answer: Option 5

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

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