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In a class, the average marks of girls in Sanskrit are 4% more than that of boys and the overall average marks in Sanskrit are 76.25. The total number of students is 60 and the ratio of number of boys to number of girls is 7 : 5. Which of the following is/are correct? I. The sum of 1/3 of average marks of boys in Sanskrit and average marks of girls in Sanskrit is a multiple of 9 II. Sum of marks of all the students in Sanskrit is a multiple of 61

In a class, the average marks of girls in Sanskrit are 4% more than that of boys and the overall average marks in Sanskrit are 76.25. The total number of students is 60 and the ratio of number of boys to number of girls is 7 : 5. Which of the following is/are correct? I. The sum of 1/3 of average marks of boys in Sanskrit and average marks of girls in Sanskrit is a multiple of 9 II. Sum of marks of all the students in Sanskrit is a multiple of 61 Correct Answer Only II

Given:

Total number of students = 60

Boys : Girls = 7 : 5

Average marks of girls in Sanskrit = 104% of average marks of boys in Sanskrit

Overall average marks in Sanskrit = 76.25

Formula Used:

Average = Sum of values/Number of values

Calculation:

Let the number of boys = 7y

Let the number of girls = 5y

7y + 5y = 60

⇒ 12y = 60

⇒ y = 5

⇒ Boys = 35

⇒ Girls = 25

Let average marks of girls in Sanskrit = a

⇒ Sum of marks of girls = 25a

Let average marks of boys in Sanskrit = b

⇒ Sum of marks of boys = 35b

Given, a = (104/100)b

⇒ a = (26/25)b

Sum of marks of all the students in Sanskrit/60 = 76.25

⇒ Sum of marks of all the students in Sanskrit = 4575

⇒ 25a + 35b = 4575

⇒ 25 × (26/25)b + 35b = 4575

⇒ 26b + 35b = 4575

⇒ 61b = 4575

⇒ b = 75

⇒ a = 78

I. The sum of 1/3 of average marks of boys in Sanskrit and average marks of girls in Sanskrit is a multiple of 9

(1/3)75 + 78 = 103

⇒ which is not a multiple of 9

⇒ I is not correct

II. Sum of marks of all the students in Sanskrit is a multiple of 61

Sum of marks of all the students in Sanskrit = 4575

⇒ 61 × 75

⇒ II is correct

∴ Only II is correct.

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