A can do a work in 36 days, B in 18 days and C in 12 days. Every 2nd day B and every 3rd day C, helps A .Then in how many days the work will be completed?

Let to work Total Work = 36
One day work of A = $$\frac{{36}}{{36}}$$ = 1 unit/day
One day work of B = $$\frac{{36}}{{18}}$$ = 2 unit/day
One day work of C = $$\frac{{36}}{{12}}$$ = 3 unit/day
In 3 days cycle total work done is A, A + B, A + C = 1 + (1 + 2) + (1 + 3) = 8 unit/Cycle
∴ 32 units of the work completed in 4 cycle and reminder 4 units of works in next two days.
1 cycle = 3 days
∴ 4 cycle = 12 days
And remaining 4 unit work done in next two days. In days 13, A will work 1 unit and in day 14, A and B will work 3 units.
Total number the day required to complete the work in the given condition is 14 days