Consider Gautam's score as 'g'. Let 'x' represent the average score of all 22 students, making the total scores of all 22 students equal to 22x.
From the initial condition: 22x - g = 21 × 62 ... (1)
Now, from the second condition: 22x - 82.5 = 21(x - 1) This simplifies to 22x - 21x = 82.5 - 21 Therefore, x = 61.5.
Substituting x = 61.5 into equation (1), we find g = 51.