Question

If $a$ and $b$ vary inversely to each other, then find the values of $p$, $q$, $r$.

Answer 1

Given: $a$ and $b$ are inversely proportional to each other.

$\Rightarrow ab=$ constant

$\Rightarrow a_1{b}_1=a_2{b}_2$

For, $a_1=6,a_2=8,b_1=18$ and $b_2=p$

$\Rightarrow 6\times 18=8\times p$

$\Rightarrow p=\frac{6\times 18}{8}=\frac{27}{2}$

Hence, the value of $p$ is $\frac{27}{2}$

Now, $a_1=6,a_2=q,b_1=18$ and $b_2=39$

$\Rightarrow 6\times 18=q\times 39$

$\Rightarrow q=\frac{6\times 18}{39}=\frac{36}{13}$

Hence, the value of $q$ is $\frac{36}{13}$

Now, $a_1=6,a_2=25,b_1=18$ and $b_2=r$

$\Rightarrow 6\times 18=25\times r$

$\Rightarrow r=\frac{6\times 18}{25}=\frac{108}{25}$

Hence, the value of $r$ is $\frac{108}{25}$