Question

If $p$, $q$ and $r$ are in proportion. Find $q$. ( $p=121$ and $r=100$)

Answer 1

Let's find $q$:

If three quantities $a$, $b$ and $c$ are in continued proportion, that is, if $a:b::b:c$, then $b^2=ac$.

It is given that, $p$, $q$ and $r$ are in proportion.

So if $p:q::q:r$, then $q^2=p\times r$.

Let's substitute $p=121$ and $r=100$ in $q^2=p\times r$:

$q^2=p\times r$

$\Rightarrow$ $q^2=121\times 100$

$\Rightarrow$$q^2=12100$

$\Rightarrow$$q^2=110\times 110$

$\Rightarrow$ $q=110$

Hence, the value of $q$ is $110$.