Question

Find the value of $x$ if the following are in continued proportion.

$12,48,x$

Answer 1

Let the three quantities are $a,b,c$

In continued proportion of three quantities, $a,b,c$ are written as $=a:b::b:c$

Let. third proportional $\left(c\right)=x$

So,

$a=12$

$b=48$

$c=x$

It is written as $12:48::48:x$

First and last term is called extreme terms, that is $12$ and $x$ and $48$ and $48$ are called middle terms.

product of extreme terms = product of middle terms.

So,

$$\begin{gathered} 12\times x=48\times 48 \\ x=\frac{48\times 48}{12} \\ x=\frac{{\displaystyle \stackrel{4}{\cancel{48}}\times 48}}{{\displaystyle \underset{1}{\cancel{12}}}} \\ x=4\times 48 \\ \therefore x=192 \end{gathered}$$

Hence the value of $x$ is $192$