The table given below shows the percentage of marks obtained by 6 students S1, S2, S3, S4, S5 and S6 in six different subjects. Students Subjects A B C S1 90 50 90 S2 75 80 80 S3 90 60 70 S4 80 65 80 S5 70 75 65 S6 65 35 50   Which of the following statement(s) is/are correct I. If the maximum marks of subject B is 150, then the average marks obtained by all the six students in subject B is 75. II. If the maximum marks of subject A is 120, then the number of students who had scored marks more than 105 is two.?

Option 4 : Only II

Given:

The maximum mark of B = 150

The maximum marks of A = 120

Concept:

The percentage of gain marks = {(The gain marks)/(The total marks)} × 100

Calculation:

⇒ From the statement l if the highest marks of B is 150 the total highest marks of 6 subjects is 900

⇒ The marks gain by B = (50 + 80 + 60 + 65 + 75 + 35) × (120/100) = 365 × 1.2 = 438

⇒ The total percentage of B = (438/900) × 100 = 48.6̅ 

⇒ So, the I statement is wrong

⇒ The second statement ll

⇒ if the highest of A is 120 then A will score marks in six subject 

⇒ S₁ = (90/100) × 120 = 108, S₂ = (75/100) × 120 = 90, S₃ =(90/100) × 120 = 108, S₄ = (80/100) × 120 = 96, S₅ = (70/100) × 120 = 84, and S₆ = (65/100) × 120 = 78

⇒ Now, there is S₁ and S₃ has more marks than 105

⇒ So, the statement ll is correct 

∴ The required result will be "Only ll".