Given that,
- In an examination,the maximum possible score $ = \text {N}$
- The passing exam score in this examination $ = \text {N} \times 45 \%$
A candidate obtain $36$ marks, but falls short of the pass marks by $ 68 \%.$ Then,
$ \text {N} \times 45\% \times (100\%-68\%)=36$
$ \Rightarrow \text {N} \times 45\% \times 32\% =36 $
$ \Rightarrow \text {N} \times \frac {45}{100} \times \frac {32}{100} = 36$
$ \Rightarrow \text {N} = 250$
We can also do that in this way,
$36 + 68\% (\text{N} \times 45\%) = \text{N} \times 45\%$
$\Rightarrow 36 + \frac{68}{100} \left(\frac{45\text{N}}{100}\right) = \frac{45\text{N}}{100}$
$\Rightarrow 36 + \frac{68}{100} \left(\frac{45\text{N}}{100}\right) -\frac{45\text{N}}{100} = 0$
$\Rightarrow \frac{45\text{N}}{100} \left( \frac{68}{100} – 1 \right) = -36$
$\Rightarrow \frac{45\text{N}}{100} \left( \frac{-32}{100} \right) = -36$
$\Rightarrow \frac{45\text{N}}{100} \left( \frac{32}{100} \right) = 36$
$\Rightarrow \frac{45\text{N}}{100} \left( \frac{8}{100} \right) = 9$
$\Rightarrow 40\text{N} = 100 \times 100$
$\Rightarrow \text{N} = \frac{1000}{4} = 250$
$\therefore $ The maximum score is in between $: 243\leq \text{N}\leq 252.$
Correct Answer $: \text {B}$