A alone can do a work in 20 days, B alone can do the same work in 30 days and C alone can do the same work in 12 days. 1st day A and B, 2nd day B and C, 3rd day C and A work and they work in the same manner. In how many days will the work be completed?

9 days

ATQ,

1st day work (by A + B) = 3 + 2 = 5

2nd day work (by B + C) = 2 + 5 = 7

3rd day work (by C + A) = 5 + 3 = 8

In 3 days total work done = 5 + 7 + 8 = 20

Therefore,

In 3 × 3 = 9 days total 20 × 3 = 60 work will be completed.