'A' requires 16 more days to finish a task compared to 'B'. When 'A' and 'B' collaborate, they complete the task in 9 days fewer than 'B' would need to finish it on his own. Determine the number of days it takes for 'A' to complete the task alone.

Let the time taken by 'B' to complete the work in 'y' days Time taken by 'A' to complete the work = (y + 16) days Time taken by them to complete the work together = (y - 9) days So, 1/y + 1/(y + 16) = 1/(y - 9)  Or, (2y + 16) X (y - 9) = y² + 16y Or, 2y² - 18y + 16y - 144 = y² + 16y Or, 2y² - 2y - 144 = y² + 16y Or, y² - 18y - 144 = 0 Or, y² - 24y + 6y - 144 = 0 Or, y(y - 24) + 6(y - 24) = 0 Or, (y + 6) (y - 24) = 0 So, 'y' = 24, or 'y' = - 6 Since number of days cannot be negative, so y = 24 Therefore, time taken by 'A' alone to complete the work = 24 + 16 = 40 days