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
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
