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A student mark was written as 80 inside of 50 so that the class average increased by 1/2.what is the total strength of the class

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Total strength of the class = 60
let class average = X        number of students = N
X N are total marks of the class.
When a students marks are written as 80 in place of 50, it means that 30 marks are added to the total marks. So the new total marks of the class is 
   X * N + 30
New average is  (X * N + 30 ) / N   
Given new average is 1/2 more than earlier one.
So    ( X N + 30 ) /  N  =  X  + 1/2
Multiply N on the R H S,                X N + 30  = X N + 1/2 N
so  1/2 N = 30      =>      N = 60
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