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.