Analyzing Student Marks and Percentages from Table Data

The problem requires us to analyze a table showing the marks obtained by 6 students in 6 different subjects. We need to find out how many students scored 60% or more marks in every single subject.

First, let's look at the provided data table:

Calculating the 60% Threshold for Each Subject

To determine if a student scored 60% or more, we first need to calculate what 60% of the maximum marks is for each subject.

• Physics (Max Marks: 100): $60\%$ of $100 = \frac{60}{100} \times 100 = 60$
• Chemistry (Max Marks: 100): $60\%$ of $100 = \frac{60}{100} \times 100 = 60$
• Math (Max Marks: 100): $60\%$ of $100 = \frac{60}{100} \times 100 = 60$
• History (Max Marks: 50): $60\%$ of $50 = \frac{60}{100} \times 50 = 30$
• Computer Science (Max Marks: 50): $60\%$ of $50 = \frac{60}{100} \times 50 = 30$
• Hindi (Max Marks: 50): $60\%$ of $50 = \frac{60}{100} \times 50 = 30$

So, the threshold marks for 60% or more in each subject are:

• Physics: 60
• Chemistry: 60
• Math: 60
• History: 30
• Computer Science: 30
• Hindi: 30

Checking Each Student's Performance Against the 60% Threshold

Now, we will check each student's marks in every subject to see if they meet or exceed the calculated 60% threshold for that subject. A student qualifies only if they score 60% or more in ALL six subjects.

• Student A:
  • Physics (80): $80 \ge 60$ (Yes)
  • Chemistry (76): $76 \ge 60$ (Yes)
  • Math (68): $68 \ge 60$ (Yes)
  • History (40): $40 \ge 30$ (Yes)
  • Computer Science (36): $36 \ge 30$ (Yes)
  • Hindi (24): $24 \ge 30$ (No)
  Student A does not meet the criteria in all subjects.
• Student B:
  • Physics (90): $90 \ge 60$ (Yes)
  • Chemistry (68): $68 \ge 60$ (Yes)
  • Math (72): $72 \ge 60$ (Yes)
  • History (42): $42 \ge 30$ (Yes)
  • Computer Science (38): $38 \ge 30$ (Yes)
  • Hindi (26): $26 \ge 30$ (No)
  Student B does not meet the criteria in all subjects.
• Student C:
  • Physics (85): $85 \ge 60$ (Yes)
  • Chemistry (81): $81 \ge 60$ (Yes)
  • Math (75): $75 \ge 60$ (Yes)
  • History (38): $38 \ge 30$ (Yes)
  • Computer Science (32): $32 \ge 30$ (Yes)
  • Hindi (31): $31 \ge 30$ (Yes)
  Student C meets the criteria in all subjects.
• Student D:
  • Physics (75): $75 \ge 60$ (Yes)
  • Chemistry (79): $79 \ge 60$ (Yes)
  • Math (58): $58 \ge 60$ (No)
  Student D does not meet the criteria in all subjects (failed in Math).
• Student E:
  • Physics (45): $45 \ge 60$ (No)
  Student E does not meet the criteria in all subjects (failed in Physics).
• Student F:
  • Physics (68): $68 \ge 60$ (Yes)
  • Chemistry (72): $72 \ge 60$ (Yes)
  • Math (68): $68 \ge 60$ (Yes)
  • History (26): $26 \ge 30$ (No)
  Student F does not meet the criteria in all subjects (failed in History).

Summary of Student Performance

Based on the analysis:

• Student A: Did not score $\ge 60\%$ in Hindi.
• Student B: Did not score $\ge 60\%$ in Hindi.
• Student C: Scored $\ge 60\%$ in ALL subjects.
• Student D: Did not score $\ge 60\%$ in Math.
• Student E: Did not score $\ge 60\%$ in Physics.
• Student F: Did not score $\ge 60\%$ in History.

Only Student C meets the condition of obtaining more than or equal to 60% marks in all subjects.

Conclusion on Number of Students with 60% in All Subjects

The number of students who obtained more than or equal to 60% marks in all subjects is 1 (Student C).

Revision Table: Key Concepts

Additional Information: Understanding Percentage in Exams

Percentage is a common way to express performance in exams. It represents the score obtained out of the total possible score, scaled to 100. The formula for calculating percentage marks is:

$\text{Percentage} = \left( \frac{\text{Marks Obtained}}{\text{Maximum Marks}} \right) \times 100\%$

In this problem, we were given the percentage threshold (60%) and the maximum marks, and we needed to find the minimum marks required to achieve that percentage: $\text{Minimum Marks} = \left( \frac{\text{Required Percentage}}{100} \right) \times \text{Maximum Marks}$. This is what we did to find the 60% threshold for each subject.

Understanding how percentages work is crucial for analyzing academic performance data. When a problem asks for performance across multiple criteria (like "all subjects"), it requires checking each criterion individually and ensuring that the student meets all of them simultaneously.