A, B and C can complete a piece of work in 4, 20 and 60 days respectively. Working together, they can complete the one third of the same work in how many days ?

Let the total work = $$T$$

$$=$$>  Work done by A in 1 day = $$\frac{\ T\ }{4}$$

$$=$$>  Work done by B in 1 day = $$\frac{\ T\ }{20}$$

$$=$$>  Work done by C in 1 day = $$\frac{\ T\ }{60}$$

$$\ \ \therefore\ $$Workdone by A,B,C together in 1 day = $$\frac{\ T}{4}+\frac{T\ }{20}+\frac{\ T\ }{60}=\frac{19}{60}T$$

$$=$$>  Number of days required for A,B,C to complete total work$$(T)$$ =$$=\ \frac{\ T}{\ \frac{\ 19}{60}T}=\frac{\ 60}{19}$$

$$=$$>  Number of days required for A,B,C to complete one third of total work$$(\frac{\ T}{3})=\frac{\ 20}{19}=\ 1\frac{\ 1}{19}$$

Hence, the correct option is Option D