Question

$6$ is the mean proportion between two numbers $x$ and $y$ and $48$ is third proportion to $x$ and $y$. Find the numbers.

Answer 1

Since, $6$ is mean proportional between $x$ and $y$.
$\Rightarrow x:6=6:y\Rightarrow xy=36$...(i)
and, $48$ is third proportional to $x$ and $y$
$\Rightarrow x:y=y:48\Rightarrow y^2=48x$...(ii)
From eq. 1; $xy=36\Rightarrow x=\frac{36}{y}$.
Substituting $x=\frac{36}{y}$ in eq. II, we get :
$y^2=48\times \frac{36}{y}\Rightarrow y^3=36\times 48$ and, $y=12$
$\therefore x=\frac{36}{y}=\frac{36}{12}=3$
$\therefore$ The required number are $3$ and $12$.