Question

N a certain class of 64 students, 30 students scored an average (arithmetic mean) of 80 marks in subject a, 20 students scored an average of 75 marks in subject a. What should be the minimum integral value of average marks scored by the remaining students so that the overall average score of the class is atleast 81 marks given that the students cannot score more than 100 marks?

Answer 1

Answer: 92

Step-by-step explanation:

Average marks = $\frac{Total marks}{Number of students}$

So, Total marks = Average marks X Number of students

With 64 students, the overall average of the class should be at least 81

So, the total marks of the class should be at least 64 X 81 = 5184          ..... 1

30 students scored an average of 80 marks

So total marks for these students = 30 X 80 = 2400          ..... 2

20 students scored an average of 75 marks

So total marks for these students = 20 X 75 = 1500          ..... 3

Remaining students = 64 - 30 - 20 = 14

From equation 1, 2 and 3, the remaining marks required from these 14 students are = 5184 - 2400 - 1500 = 1284

So the average marks of the 14 students should be at least = $\frac{1284}{14}$ = 91.7

Since the question asks for the minimum integral value, the answer is rounded off to 92.