A, B and C can do a piece of work in 10, 20 and 30 days, respectively. In how many days can A do the work if he is assisted by B and C on every third day?

A, B and C can do a piece of work in 10, 20 and 30 days, respectively.

Let's assume the total work is 60 units.

Efficiency of A = $$\frac{60}{10}\ = 6$$ units/day

Efficiency of B = $$\frac{60}{20}\ = 3$$ units/day

Efficiency of C = $$\frac{60}{30}\ = 2$$ units/day

A start the work and he is assisted by B and C on every third day.

So work done on the first day = 6 units

work done on the second day = 6 units

work done on the third day = (6+3+2) units = 11 units

Work done in first three days = 6+6+11 = 23

By this way the work done in the first eight days = 23+23+6+6

= 58 units

So after eight days, [(60-58) = 2] units of work is remaining which can be done by all of them together in $$\frac{2}{11}$$ days.

Hence the time is taken to complete the work = $$8+\frac{2}{11}$$

= $$8\frac{2}{11}$$ days