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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
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