The following table shows the marks scored by six students (A–F) in six different subjects S1 to S6 having maximum marks of 160, 160, 120, 120, 200, and 240 respectively. Based on the data in the table, answer the question that follows: Student-wise details of Marks ScoredStudents Marks Scored in Subject S1 (Out of 160) S2 (Out of 160) S3 (Out of 120) S4 (Out of 120) S5 (Out of 200) S6 (Out of 240) A 76 84 66 56 154 144 B 120 100 84 76 136 132 C 128 72 64 70 144 160 D 84 130 96 84 104 168 E 64 128 90 92 174 70 F 70 96 60 56 164 96
Determining First Division Eligibility Based on Aggregate Marks
The question requires us to identify the number of students who have achieved a 'first division'. The specific criterion for obtaining a first division is scoring a minimum of 60% marks in aggregate across all subjects.
Calculating Total Maximum Aggregate Marks
First, we must calculate the total maximum possible marks a student can achieve. This is done by summing the maximum marks designated for each of the six subjects (S1 through S6).
The calculation for total maximum marks is as follows:
Total maximum marks = Maximum marks in S1 + Maximum marks in S2 + Maximum marks in S3 + Maximum marks in S4 + Maximum marks in S5 + Maximum marks in S6
Using LaTeX notation for clarity:
Total maximum marks = $160 + 160 + 120 + 120 + 200 + 240 = 1000$ marks.
Calculating Minimum Aggregate Marks for First Division
Next, we determine the minimum aggregate marks needed to qualify for a first division. This is calculated as 60% of the total maximum aggregate marks.
The formula is:
Minimum aggregate marks = 60% of Total maximum marks
Using LaTeX for the calculation:
Minimum aggregate marks = $\frac{60}{100} \times 1000 = 0.60 \times 1000 = 600$ marks.
Therefore, a student must score 600 marks or more in total to be eligible for the first division.
Student Performance Summary
We will now calculate the total marks obtained by each student across all six subjects. Subsequently, we will compare each student's total score against the 600-mark threshold for the first division.
| Student | Total Marks Scored | Meets First Division Criteria (>= 600) |
|---|---|---|
| A | $76 + 84 + 66 + 56 + 154 + 144 = 580$ | No |
| B | $120 + 100 + 84 + 76 + 136 + 132 = 648$ | Yes |
| C | $128 + 72 + 64 + 70 + 144 + 160 = 638$ | Yes |
| D | $84 + 130 + 96 + 84 + 104 + 168 = 666$ | Yes |
| E | $64 + 128 + 90 + 92 + 174 + 70 = 618$ | Yes |
| F | $70 + 96 + 60 + 56 + 164 + 96 = 542$ | No |
Counting Students Achieving First Division
After calculating the total marks for each student, we compare these totals with the required minimum of 600 marks.
- Student A achieved 580 marks, which is less than 600.
- Student B achieved 648 marks, which is greater than or equal to 600.
- Student C achieved 638 marks, which is greater than or equal to 600.
- Student D achieved 666 marks, which is greater than or equal to 600.
- Student E achieved 618 marks, which is greater than or equal to 600.
- Student F achieved 542 marks, which is less than 600.
Based on these results, students B, C, D, and E meet the criteria for the first division.
Therefore, the total number of students securing a first division is 4.
Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
The numbers of students of three classes of a school are in the ratio 4 : 5 : 6. If numbers of students in these classes increase by 25%, 20% and 25% respectively, then ratio of numbers of students will become:
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
