Akbar can complete a piece of work alone in 12 days, while Anthony can complete the same work alone in 20 days. If they work on alternate days with Anthony starting the work, then in how many days can they complete the whole work?

Let's assume the total work is 60 units.

Akbar can complete a piece of work alone in 12 days.

Efficiency of Akbar = $$\frac{60}{12}$$ = 5 units/day

while Anthony can complete the same work alone in 20 days.

Efficiency of Anthony = $$\frac{60}{20}$$ = 3 units/day
If they work on alternate days with Anthony starting the work.

Work done by Anthony on first day = 3 units

Work done by Akbar on second day = 5 units

Work done by them in first two days = (3+5) = 8 units

Work done by them in first 14 days = $$8\times7$$ = 56 units

Now the remaining work is (60-56) = 4 units.

Now on 15th day Anthony will do 3 units of work and at the end of 15th day, 1 unit of work is remaining which will be done by Akbar on the next day.

So the time taken to complete the whole work by working on alternate days = $$14+1+\frac{1}{5}$$

= $$15\frac{1}{5}$$ days