A student secured 20% marks in a competitive examination. 30 more marks were required to pass it. Another student secured 32% marks. This is 42 more than the pass mark. What is the... A student secured 20% marks in a competitive examination. 30 more marks were required to pass it. Another student secured 32% marks. This is 42 more than the pass mark. What is the maximum marks for this examination?
Understand the Problem
The question describes a scenario involving two students' scores in an exam and asks to calculate the maximum possible marks for the exam, given that the first student scored 20% and needed 30 more marks to pass, while the second student scored 32%, which was 42 more than the pass mark.
Answer
A) 600
Answer for screen readers
A) 600
Steps to Solve
- Define variables
Let $x$ be the maximum marks for the examination.
Let $p$ be the pass mark.
- Express the given information as equations
The first student secured 20% of the marks, and needed 30 more to pass. Therefore: $0.20x + 30 = p$
The second student secured 32% of the marks, which was 42 more than the pass mark. Therefore: $0.32x = p + 42$
- Solve the system of equations
We can substitute the first equation into the second equation to eliminate $p$:
$0.32x = (0.20x + 30) + 42$
- Simplify the equation
$0.32x = 0.20x + 72$
- Solve for $x$
Subtract $0.20x$ from both sides:
$0.12x = 72$
Divide both sides by $0.12$:
$x = \frac{72}{0.12} = \frac{7200}{12} = 600$
A) 600
More Information
The maximum marks for the examination are 600. We can find the passing score by substituting x = 600 into the first equation: Pass mark $ = 0.20 * 600 + 30 = 120 + 30 = 150 $
Also, by substituting x = 600 into the second equation: $ 0.32 * 600 = 192 $. $ 192 - 42 = 150 $ which is the passing score as well.
Tips
A common mistake is to incorrectly set up the equations based on the given information, for example, adding 30 to the passing score for the first student or subtracting 42 from the passing score for the second student. Careful reading and understanding of the problem statement are crucial to avoid this.
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