"Rahul" and "Sohan" have respective completion times of 15 and 25 days for a task. They began working together on the project, but after a few days, "Rahul" left and "Priya," who can finish the entire task on her own in 12 days, joined. Three days before the job was finished, "Priya" left. Determine the amount of work completed by "Sohan" if "Rahul" and "Priya" worked for a similar number of days.

Rahul's work rate: 1/15 task per day

Sohan's work rate: 1/25 task per day

Priya's work rate: 1/12 task per day

Let:

x = Number of days Rahul and Priya worked.

Total time taken to complete the task = T days.

Rahul: Worked for x days.

Work done = x/15.

Sohan: Worked for the entire T days.

Work done = T/25

Priya: Worked for x days but 3 days before the task was completed.

Work done = (x - 3)/12

The total work done is equal to 1 the entire task. So:

x/15 + T/25 + (x - 3)/12 = 1

Since Rahul and Priya worked for the same number of days x, and Priya 3 days before the task was completed:

T = x + (x - 3) = 2x - 3

Substitute T = (2x - 3) into the Work Equation

x/15 + (2x - 3)/25 + (x - 3)/12 = 1

Multiply through by 300 LCM of 15, 25, and 12 to eliminate denominators:

20x + 12(2x - 3) + 25(x - 3) = 300

20x + 24x - 36 + 25x - 75 = 300

69x - 111 = 300

69x = 411

x = 411 / 69 = 6

T = 2x - 3 = 2(6) - 3 = 9

Sohan worked for the entire T = 9 days.

Work done by Sohan = 9/25

The amount of work completed by Sohan is 9/25.