# In a class of 51 students, the difference between the highest mark and the least mark is 70.

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In a class of 51 students, the difference between the highest mark and the least mark is 70. If the average score is calculated without considering the student who got the highest mark, then the average score decreases by 1%. If the average score is calculated without considering the student who got the least mark, then the average score increases by 1.33%. What is the original average score of the class?

1. 60
2. 70
3. 80
4. 40

Let the average mark be x.

Total marks = 51x

50 * 0.99x = 51x - max

50 * 1.0133x = 51x - min

Subtracting last two,

50* 0.0233x = max - min = 70,

x = 60
let say t= total marks (addition of all the marks).

here we have given 51 students (n=51)

let say the average is x.

so according to the standard formula of finding the average   t/n=x

t=51x.

now, we can use any of the conditions

according to case one:

t-90/(51-1)=x-0.01x

now take t=51x and solve it

51x-90/(50)=0.99x

x=60.

here we get the same answer from the case 2 as well.

1.60

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