Correct Answer - Option 2 : 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.