Question

Q5. The average score of 35 students in a class is 37. If every student is given 3 grace
marks, the new average of the class is​

Answer 1

Answer:

The average score of 35 students in a class is 37. If every student is given 3 grace marks, the new average of the class is: A. 45

Answer 2

Correct Question: The average score of 35 students in a class is 37. If every student is given 3 grace marks, the new average of the class is:

(a) 45

(b) 34

(c) 43

(d) 40

(e) None of these

Correct answer is option (d) 40.

Given:

The total number of students in the class (n) = 35

The average score of 35 students (avg) = 37

Grace mark given to each student = 3

To Find:

In order to find the new average of the class, we have to know,

1. The total marks of 35 students.

2. The total marks of 35 students after giving grace marks.

Solution:

We use the following equation to find out the total marks of 35 students.

Total marks = Average mark × Total number of students.

Substituting the values in above equation, we get,

Total mark = $37$ × $35$

= $1295.$

If every student is given 3 grace marks, the total grace marks obtained for 35 students is given by,

Total grace marks = Grace mark given to each student × Total number of students.

Total grace marks = $3$ × $35$

= $105.$

Now we have to calculate the total marks of 35 students after giving grace marks or the new total mark.

Total mark after giving grace marks = Total grace marks + Total mark before giving grace marks.

Total mark after giving grace marks = $105 + 1295$

= $1400.$

Therefore, the new average of the class is,

New average = $\frac{New Total mark}{Total number of students}$

= $\frac{1400}{35}$

= $40.$

Hence, the new average of the class is​ 40.