Two individuals, P and Q, can complete a task in (x + 6) days and (x + 3) days, respectively. Another individual, S, is capable of completing 25% of the same task in 9 days. When P and S work together, they can complete the entire task in 12 days. Determine the time required for P and Q to complete the task together.

Total time taken by 'S' to complete the work = 9 x (100/25) = 36 days Let the total work be 360 units (L.C.M. of 36 days and 12 days) Efficiency of 'S' = (360/36) = 10 units/day Combined efficiency of 'P' and 'S' = (360/12) = 30 units/day So, the efficiency of 'P' = 30 - 10 = 20 units/day Time taken by 'P' to complete the work alone = (360/20) = 18 days ATQ, (x + 6) = 18 days So, 'x' = 12 So, number of days taken by 'Q' = (x + 3) = (12 + 3) = 15 days So, efficiency of 'Q' = (360/15) = 24 units/day Therefore, required number of days = {360 ÷ (20 + 24) } = (90/11) days