Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2006 · Marks: · Difficulty:
Find the two numbers whose mean proportion is 12 and the third proportional is 324.
(a)6 and 8
(b)4 and 36
(c)3 and 24
(d)None of these
Answer
Answer (as printed): B
Explanation
Let the two numbers be $x$ and $y$. Then, $\sqrt{x y}=12$ and $x: y:: y: 324$ $$\begin{aligned} & \Rightarrow x y=(12)^{2}=144 \text { and } y^{2}=324 x \\ & \Rightarrow x=\frac{144}{y} \text { and } y^{2}=324 \times \frac{144}{y} \\ & \Rightarrow y^{3}=324 \times 144=(6 \times 3 \times 2)^{3} \Rightarrow y=6 \times 3 \times 2=36 \\ & \Rightarrow x=\frac{144}{36}=4 . \end{aligned}$$ Hence, the two numbers are 4 and 36.
Explanation as extracted from the printed page; notation may be imperfect.