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?

Let B's 1 day's work = $$2x$$ units/day

=> A's 1 day's work = $$1.5\times2x=3x$$ units/day

Let B takes $$d$$ days, => A takes $$(d-8)$$ days to finish the work.

=> Total work = $$2x\times d=3x\times(d-8)$$

=> $$2d=3d-24$$

=> $$d=24$$

$$\therefore$$ Total work = $$2x\times24=48x$$ units

If A and B work on alternate days and A works on first day, => Work done in 2 days = $$3+2=5$$ units

Multiplying both sides by 9, => Work done in 18 days = 45 units

Now, its A's turn to do the work, thus he will do the remaining 3 units on the 19th day.

=> Ans - (B)