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.

Answer : x=60.