Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2008 · Marks: · Difficulty:
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 numbers be $x$ and $y$. Then, $\frac{1}{4}$ of (60\% of $x$ ) $=\frac{2}{5}$ of (20\% of $y$ ) $$\begin{aligned} & \Rightarrow\left(\frac{1}{4} \times \frac{60}{100} \times x\right)=\left(\frac{2}{5} \times \frac{20}{100} \times y\right) \Rightarrow \frac{3 x}{20}=\frac{2 y}{25} \\ & \Rightarrow \frac{x}{y}=\frac{2}{25} \times \frac{20}{3}=\frac{8}{15} \Rightarrow x: y=8: 15 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.