A student secured 20% marks in a competitive examination. 30 more marks were required to pass it. Another student secured 32% marks, which is 42 more than the pass mark. What is th... A student secured 20% marks in a competitive examination. 30 more marks were required to pass it. Another student secured 32% marks, which is 42 more than the pass mark. What is the maximum marks for this examination?
Understand the Problem
The question is a word problem involving percentages and requires us to find the maximum marks for an examination. We are given that one student secured 20% of the marks and needed 30 more marks to pass, while another student secured 32% of the marks, which was 42 more than the pass mark. We will need to use this information to set up equations and solve for the maximum marks.
Answer
A) 600
Answer for screen readers
A) 600
Steps to Solve
- Define variables
Let $x$ be the maximum marks for the examination, and let $p$ be the pass mark.
- Write the equation for the first student
The first student secured 20% of the marks and needed 30 more marks to pass. We can write this as: $0.20x + 30 = p$
- Write the equation for the second student
The second student secured 32% of the marks, which was 42 more than the pass mark. We can write this as: $0.32x = p + 42$
- Solve for $p$ in the first equation
From the first equation, we have: $p = 0.20x + 30$
- Substitute the value of $p$ into the second equation
Substituting $p = 0.20x + 30$ into the second equation, we get: $0.32x = (0.20x + 30) + 42$
- Simplify and solve for $x$
Simplify the equation: $0.32x = 0.20x + 72$
Subtract $0.20x$ from both sides: $0.12x = 72$
Divide both sides by 0.12: $x = \frac{72}{0.12} = \frac{7200}{12} = 600$
Therefore, the maximum marks for the examination is 600.
A) 600
More Information
The maximum marks for the examination are 600. The pass mark would be $0.20 * 600 + 30 = 120 + 30 = 150$. The second student scored $0.32 * 600 = 192$, which is $150 + 42 = 192$, confirming our answer.
Tips
A common mistake would be setting up the equations incorrectly, or making a mistake in algebraic manipulation when solving the equations. For example, forgetting to distribute when substituting or incorrectly dividing.
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