Ajay, Vijay and Sashi can do a piece of work in 20, 40 and 60 days, respectively. In how many days can Ajay do the work if he is assisted by Vijay and Sashi on every fourth day?

Let's assume the total work is 120 units.

Ajay, Vijay and Sashi can do a piece of work in 20, 40 and 60 days, respectively.

Efficiency of Ajay = $$\frac{120}{20}$$ = 6 units/day

Efficiency of Vijay = $$\frac{120}{40}$$ = 3 units/day

Efficiency of Sashi = $$\frac{120}{60}$$ = 2 units/day

Work done by Ajay in first 3 days = $$6\times3$$ = 18 units

Work done by all of them on 4th day = 6+3+2 = 11 units

Work done by them in the first four days = 18+11 = 29 units

Work done by them in the first 16 days = $$29\times4$$ = 116 units

On 17th day, 120-116 = 4 units of work is remaining. These four units can be done by Ajay in $$\frac{4}{6}$$ days.

Time taken by Ajay do the work if he is assisted by Vijay and Sashi on every fourth day = $$16\frac{4}{6}$$

= $$16\frac{2}{3}$$

= $$\frac{50}{3}$$ days