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?
(a)4: 7
(b)5: 9
(c)8: 13
(d)Cannot be determined
(e)None of these
Answer
Answer (as printed): E
Explanation
Let the first number be $x$ and the second number be $y$. Then, $$\begin{aligned} & \frac{1}{4} \text { of } 60 \% \text { of } x=\frac{2}{5} \text { of } 20 \% \text { of } y \\ & \Rightarrow \frac{1}{4} \times \frac{60}{100} \times x=\frac{2}{5} \times \frac{20}{100} \times y \Rightarrow \frac{3 x}{20}=\frac{2 y}{25} \\ & \Rightarrow \frac{x}{y}=\frac{2}{25} \times \frac{20}{3}=\frac{8}{15} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.