A is 1.5 times efficient than B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed?

A is 1.5 times efficient as B, so A's work: B's work = 3:2. Let A take x days, B takes x+8 days. Work ratio gives (x+8)/x = 3/2, so 2x+16 = 3x, x = 16. A takes 16 days, B takes 24 days. Total work = LCM(16,24) = 48 units. A/day = 3, B/day = 2. Working alternately starting with A for 10 days (5 cycles): work = 5×(3+2) = 25 units. Remaining 23 units: day 11 (A) does 3, day 12 (B) does 2, day 13 (A) does 3, day 14 (B) does 2, day 15 (A) does 3, day 16 (B) does 2, day 17 (A) does 3, day 18 (B) does 2, day 19 (A) does remaining 3. Total 19 days.