In an examination a candidate who got 30% of the total marks failed by 8 marks. Another candidate who got 35% got 12 marks more than the passing marks. Total marks are?

1. A

   500

2. B

   400

3. C

   800

4. D

   300

Appeared in: DHS 2018 shift 1st

Explanation

• The problem can be solved by setting up a linear equation where the 'passing marks' are expressed in two different ways based on the data for each candidate.
• The first candidate's score (30% of total) plus 8 marks equals the passing mark.
• The second candidate's score (35% of total) minus 12 marks also equals the passing mark.
• Equating these two expressions reveals that the 5% difference in their scores (35% - 30%) corresponds to a 20-mark difference (8 marks below passing + 12 marks above passing).
• If 5% of the total marks is 20, then the total marks (100%) are calculated as (20 / 5) * 100, which equals 400.

Why Other Options Were Wrong

• Option A: If the total marks were 500, the passing marks calculated from both candidates' scores would not match. Candidate 1: (0.30 * 500) + 8 = 158. Candidate 2: (0.35 * 500) - 12 = 163. Since 158 is not equal to 163, this option is incorrect.
• Option C: If the total marks were 800, the passing marks would be inconsistent. Candidate 1: (0.30 * 800) + 8 = 248. Candidate 2: (0.35 * 800) - 12 = 268. Since 248 is not equal to 268, this option is incorrect.
• Option D: If the total marks were 300, the passing marks would be inconsistent. Candidate 1: (0.30 * 300) + 8 = 98. Candidate 2: (0.35 * 300) - 12 = 93. Since 98 is not equal to 93, this option is incorrect.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Quantitative Aptitude - Percentages as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude and logical reasoning, which are essential skills assessed in the general intelligence and aptitude sections of many competitive nursing entrance examinations.
• While not a clinical question, the ability to perform calculations accurately and think logically is crucial for nurses in tasks such as medication dosage calculation, interpreting vital signs, and managing patient data.
• What if the first candidate had failed by 10 marks and the second got 10 marks more? The total difference would still be 20 marks (10+10), and the 5% difference in score would still correspond to 20 marks, leading to the same answer of 400 total marks.

How to Approach the Question

• First, carefully read the problem and identify the key pieces of information: the percentages, the marks deficit (failed by), and the marks surplus (more than).
• Recognize that the 'passing mark' is the constant element that connects the two candidates' scores. Define it as a variable.
• Translate the information for each candidate into an algebraic expression for the passing mark in terms of the total marks (T).
• Set the two expressions equal to each other. This creates a single equation with one unknown variable (T).
• Solve the linear equation for T to find the total marks.
• Alternatively, use the shortcut: calculate the difference in percentages and the total difference in marks (sum of deficit and surplus), then equate them to find the value of 1% and subsequently 100%.

Concept Tested & Keywords

• Concept Tested: Quantitative Aptitude - Percentages
• Stem keywords: percentage, total marks, failed by, more than passing marks
• Lead-in keywords: Total marks are?

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QOzk5hl5I8TFtoAXsuwpp9

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