Let the total number of students appeared be n And let the sum of marks of total student be S ∴ average marks = S/n = 50 ⇒ S = 50n ...........Equation. (1) Now, after deducting 30 marks as the score is reduced from 90 to 60 of 100 students, the new sum of marks = S - 3000 ∴ new average = (S - 3000)/n But new average = 45 So, (S - 3000)/n = 45 Now, from equation. (1), we know that S = 50n ⇒ 50n - 3000 = 45n ⇒ n = 3000/5 = 600 ∴ total number of students who appeared for an exam = 600