Question

The average marks obtained by 40 students of a class is 85. The difference between the marks
obtained by the student who get the highest mark and the student who get the lowest mark is
108. If both these students are removed, the average falls by 1 mark. Find the highest mark.
1) 144
2) 158
3) 172
4) cannot be determined​

Answer 1

||✪✪ QUESTION ✪✪||

The average marks obtained by 40 students of a class is 85. The difference between the marks

obtained by the student who get the highest mark and the student who get the lowest mark is

108. If both these students are removed, the average falls by 1 mark. Find the highest mark.

1) 144

2) 158

3) 172

4) cannot be determined

|| ✰✰ ANSWER ✰✰ ||

we know That :-

→ Average = ( sum of All observation) / (Total Number of observation ).

it has been given That, average marks of 40 students is 85.

That Means , we can say That,

→ Total marks of all The students is = 40 * 85 = 3400 -------------- Equation (1).

______________________

Now, when The two students with Highest and lowest marks were Removed ,

→ Total Students Left in class = 40 - 2 = 38

→ New Average now = 85 - 1 = 84 .

So,

→ Total Marks of these 38 students = 38 * 84 = 3192. -------------- Equation (2).

______________________

Now, we can say That, if we subtract , Equation (2), From Equation (1), we will get Total marks of Those Two students .

So,

→ 2 Students Total marks = 3400 - 3192 = 208 .

______________________

Now, We have Given That, Difference b/w their marks is 108.

→ Let Highest Marks of student = x

→ Lowest mark of student = y

Than,

→ x + y = 208

→ x - y = 108

Adding both ,

→ 2x = 316

Dividing both sides by 2,

→ x = 158 .

Putting This value now, we get,

→ y = 208 - 158 = 50.

Hence, We can say That, The Highest Marks of student is 158. (Option 2).

Answer 2

Option 2) is correct......