1. Problem statement: The maximum possible score is $N$, and the pass mark is $45\%$ of $N$, i.e., $0.45N$. 2. A candidate obtains 36 marks but falls short of the pass mark by 68%. This means the candidate's marks are $68\%$ less than the pass mark. 3. Let the pass mark be $P = 0.45N$. 4. The candidate's score is $36$, which is $68\%$ less than $P$. Mathematically, $36 = P - 0.68P = 0.32P$. 5. Substitute $P = 0.45N$ into the equation: $$36 = 0.32 \times 0.45N = 0.144N$$ 6. Solve for $N$: $$N = \frac{36}{0.144} = 250$$ 7. Compare $N$ to the given options: - A) $N \leq 200$ (False since $250 > 200$) - B) $243 \leq N \leq 252$ (True because $250$ is within this range) - C) $201 \leq N \leq 242$ (False) - D) $N \geq 253$ (False) - E) None of these (False) **Answer: Option B) $243 \leq N \leq 252$**