N and T can complete typing of 2000 letters in 18 days and N works at a half of speed of the speed of T. If T leaves N 12 days after they both started working, then how many days delay will take place in completing this work?

N's speed is half of T's speed. Let T's rate = 2x letters/day, N's rate = x letters/day. Combined rate = 3x letters/day. Together for 12 days: 36x letters completed. Remaining: 2000 - 36x letters. N works alone at rate x: time = (2000 - 36x)/x = 2000/x - 36 days. Total time = 12 + 2000/x - 36 = 2000/x - 24 days. Normal time at combined rate: 2000/(3x) days. Delay = (2000/x - 24) - (2000/(3x)) = (4000/(3x) - 24). From 18 days together at rate 3x: 54x = 2000, x = 1000/27. Delay = 4000/(3×1000/27) - 24 = 36 - 24 = 12 days.