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
The question asks us to compare the combined marks of two pairs of students in subject S1 and express the difference as a percentage. We need to find how much more the marks scored by student B and student C together are, compared to the marks scored by student A and student D together in subject S1.
Student Marks in Subject S1
First, let's extract the relevant marks from the provided table for subject S1:
- Marks scored by Student A in S1: 76
- Marks scored by Student B in S1: 120
- Marks scored by Student C in S1: 128
- Marks scored by Student D in S1: 84
Calculating Combined Marks
Next, we calculate the combined marks for the two groups:
- Combined marks for Student B and Student C in S1: $120 + 128 = 248$
- Combined marks for Student A and Student D in S1: $76 + 84 = 160$
Percentage Comparison Calculation
Now, we need to find the percentage by which the combined marks of B and C are more than the combined marks of A and D. We use the following formula:
Percentage Increase $= \frac{\text{Marks}(B+C) - \text{Marks}(A+D)}{\text{Marks}(A+D)} \times 100$
Let's plug in the values:
Percentage Increase $= \frac{248 - 160}{160} \times 100$
Percentage Increase $= \frac{88}{160} \times 100$
To simplify the fraction $\frac{88}{160}$, we can divide both the numerator and the denominator by their greatest common divisor. Both are divisible by 8:
$\frac{88 \div 8}{160 \div 8} = \frac{11}{20}$
Now, convert the fraction to a percentage:
Percentage Increase $= \frac{11}{20} \times 100$
Percentage Increase $= 11 \times \frac{100}{20}$
Percentage Increase $= 11 \times 5 = 55\%$
Conclusion
The marks scored by student B and student C together in subject S1 are 55% more than the marks scored by student A and student D together in the same subject.
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:
