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
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 ;
