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In an examination, the maximum possible score is $\text{N}$ while the pass mark is $45\%$ of $\text{N}$. A candidate obtains $36$ marks, but falls short of the pass mark by $68\%$. Which one of the following is then correct?

1. $\text{N} \leq 200$
2. $243\leq \text{N} \leq 252$
3. $\text{N} \geq 253$
4. $201 \leq \text{N} \leq 242$

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 $: \text {B}$

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