Question

For the following table of marks (in percentages) of 5 students in Maths, Physics and Chemistry.

Here 400 marks for each subject, which of the following is difference of marks between the highest marks and lowest marks in any subject of any student?}

• A. 316
• B. 192
• C. 124
• D. 148

Hint:

To avoid working with large numbers, always compute the percentage difference first and then convert it into actual marks at the very end.
This saves extra multiplication steps!

Answer 1

The Correct Option is D

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Step 1: Understanding the Question: This question involves analyzing percentage values in a table.
The maximum marks for each subject are 400.
We need to find the absolute highest percentage scored by any student in any subject and the absolute lowest percentage scored by any student in any subject, calculate their difference in percentage, and then find the corresponding marks.

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Step 2: Key Formula or Approach:
1. Scan the entire table to find:
\[ P_{\text{max}} = \text{Maximum percentage in the entire table} \]
\[ P_{\text{min}} = \text{Minimum percentage in the entire table} \]
2. Difference in marks:
\[ \text{Difference} = (P_{\text{max}} - P_{\text{min}})\% \times 400 \]
Alternatively, calculate the marks individually and then subtract.

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Step 3: Detailed Explanation:
- Let us identify the highest percentage in the table:
By looking at all values:
Maths: 75, 81, 53, 79, 59
Physics: 70, 85, 79, 48, 53
Chemistry: 79, 70, 48, 81, 64
The absolute maximum value is 85% (scored by student 2 in Physics).
So, \(P_{\text{max}} = 85\%\).
- Let us identify the lowest percentage in the table:
The absolute minimum value is 48% (scored by student 4 in Physics and student 3 in Chemistry).
So, \(P_{\text{min}} = 48\%\).
- Now, let us calculate the percentage difference:
\[ \text{Percentage difference} = 85\% - 48\% = 37\% \]
- Since the maximum marks for each subject are 400, the absolute difference in marks is:
\[ \text{Difference in marks} = 37\% \text{ of } 400 = \frac{37}{100} \times 400 \]
\[ \text{Difference in marks} = 37 \times 4 = 148 \]
Let us double check with individual calculations:
- Highest marks = \(85\% \text{ of } 400 = 340\)
- Lowest marks = \(48\% \text{ of } 400 = 192\)
- Difference = \(340 - 192 = 148\)
The two methods yield the exact same answer.

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Step 4: Final Answer: The difference in marks is 148, which is option (D).