Worker 'A' takes 16 more days than the combined time

Solution

Let the time taken by 'A' and 'B' to do the work together be 'x' days So, time taken by 'A' alone to do the work = (x + 16) days So, (1/x) = {1/(x + 16)} + (1/60) Or, x(x + 16 + 60) = 60 X (x + 16) Or, x² + 76x = 60x + 960 Or, x² + 16x - 960 = 0 Or, x² + 40x - 24x - 960 = 0 Or, x(x + 40) - 24(x + 40) = 0 Or, (x + 40)(x - 24) = 0 So, x = 24 or x = -40 So, time taken by 'A' to do the work alone = 24 + 16 = 40 days And, time taken to do 125% of the work = 40 X 1.25 = 50 days