Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2006 · Marks: · Difficulty:
Seeta and Geeta have two glasses of equal volumes. Both have some milk in their glasses. Seeta says to Geeta. "Give me half the milk in your glass so that my glass will be full of milk." Geeta says to Seeta, "Instead you give me one-fourth of the milk in your glass so that my glass will be full of milk." Find the ratio of volumes of milk in their glasses.
(a)1 : 2
(b)4 : 3
(c)3 : 4
(d)2 : 3
Answer
Answer (as printed): D
Explanation
Let the capacity of each glass be $z$. Let $x$ and $y$ denote the quantities of milk in glasses of Seeta and Geeta respectively. Then, $x+\frac{1}{2} y=z$ and $$y+\frac{1}{4} x=z$$ So, $x+\frac{1}{2} y=y+\frac{1}{4} x \Rightarrow \frac{3}{4} x=\frac{1}{2} y \Rightarrow \frac{x}{y}=\frac{1}{2} \times \frac{4}{3}=\frac{2}{3}$. Hence, required ratio = 2 : 3.
Explanation as extracted from the printed page; notation may be imperfect.