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
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
