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
Calculating the Ratio of Student Marks
The question asks for the ratio of the total marks scored by student B to the total marks scored by student D, based on the provided table of scores across six subjects.
Student Marks Data
First, let's extract the marks scored by Student B and Student D in each subject:
| Student | S1 | S2 | S3 | S4 | S5 | S6 |
| B | 120 | 100 | 84 | 76 | 136 | 132 |
| D | 84 | 130 | 96 | 84 | 104 | 168 |
Calculating Total Marks for Student B
To find the total marks scored by Student B, we sum the marks obtained in all six subjects:
Total Marks (B) = Marks(S1) + Marks(S2) + Marks(S3) + Marks(S4) + Marks(S5) + Marks(S6)
Total Marks (B) = $120 + 100 + 84 + 76 + 136 + 132$
Total Marks (B) = $648$
Calculating Total Marks for Student D
Similarly, we sum the marks obtained by Student D in all six subjects:
Total Marks (D) = Marks(S1) + Marks(S2) + Marks(S3) + Marks(S4) + Marks(S5) + Marks(S6)
Total Marks (D) = $84 + 130 + 96 + 84 + 104 + 168$
Total Marks (D) = $666$
Determining the Ratio
The question requires the ratio of the total marks scored by Student B to the total marks scored by Student D. This can be written as:
Ratio (B : D) = Total Marks (B) : Total Marks (D)
Ratio (B : D) = $648 : 666$
Simplifying the Ratio
To simplify the ratio $648 : 666$, we need to find the greatest common divisor (GCD) of 648 and 666.
- Prime factorization of 648: $2^3 \times 3^4$
- Prime factorization of 666: $2 \times 3^2 \times 37$
- The GCD is $2 \times 3^2 = 2 \times 9 = 18$.
Now, divide both parts of the ratio by the GCD (18):
Simplified Ratio = $\frac{648}{18} : \frac{666}{18}$
Simplified Ratio = $36 : 37$
Therefore, the ratio of the total marks scored by student B to the total marks scored by student D is $36 : 37$.
Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
