Discussion
A candidate scores 20% and fails by 45 marks and another candidate who scores 45% marks gets 30 marks more than the minimum required to pass the examination. Find the maximum marks for the examination.
Answer: D
The maximum marks are 300.
Let the maximum be M. The pass mark is 45 more than 20% of M, and also 30 less than 45% of M:
\[ \begin{aligned} 0.20M + 45 &= 0.45M - 30 \\ 0.25M &= 75 \\ M &= 300 \end{aligned} \]
Check: the pass mark is 105. The first candidate scores 60 and falls short by 45; the second scores 135, which is 30 above the pass mark.
With 100, 200 or 400 the two descriptions of the pass mark disagree; for example 400 gives 125 from the first and 150 from the second.
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