Two students appeared for an examination. One of them scored 25 marks more than the other and his marks was 60 percent of the sum of their marks. What was the total marks obtained by them?

1. A

   100 percent

2. B

   125 percent

3. C

   120 percent

4. D

   75 percent

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

• The problem requires setting up two linear equations with two variables to represent the two students' marks.
• Let the marks be x and y. The equations are: x = y + 25 and x = 0.6 * (x + y).
• Solving this system of equations reveals that the marks are 75 and 50.
• The sum of these marks (75 + 50) gives the total marks, which is 125.

Why Other Options Were Wrong

• Option A: If the total marks were 100, the higher scorer would have 60% of 100, which is 60 marks. The other student would have 40 marks. The difference is 20 (60 - 40), not 25 as stated in the problem.
• Option C: If the total marks were 120, the higher scorer would have 60% of 120, which is 72 marks. The other student would have 48 marks. The difference is 24 (72 - 48), which is very close but not the required 25.
• Option D: This value represents the marks of the higher-scoring student (x = 75), not the total marks of both students combined.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations from a word problem as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude and logical reasoning, which are foundational skills for nurses.
• Nurses frequently use mathematical skills for tasks such as calculating medication dosages, determining IV drip rates, and interpreting patient data, all of which require precision and the ability to work with percentages and formulas.
• What if the higher score was 75% of the total marks? The equation would change to x = 0.75 * (x + y). Solving this new system would yield x=75 and y=25, for a total of 100 marks. This demonstrates how changing a single percentage can significantly alter the outcome.

How to Approach the Question

• First, carefully read the word problem to understand what is given and what is being asked. Identify the key numerical relationships.
• Assign variables to the unknown quantities. For instance, let 'x' and 'y' be the marks of the two students.
• Translate the sentences from the problem into mathematical equations. Each piece of information usually corresponds to one equation.
• You will have a system of two equations. Use substitution or elimination methods to solve for one of the variables.
• Once one variable is found, substitute its value back into one of the original equations to find the other variable.
• Finally, calculate the value requested by the question (in this case, the sum of the marks) and double-check your answer by plugging the values back into the original problem statement to ensure they hold true.

Concept Tested & Keywords

• Concept Tested: Solving linear equations from a word problem.
• Stem keywords: examination, scored 25 marks more, 60 percent of the sum, total marks
• Lead-in keywords: What was

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