Question

The team of A B and C was supposed to complete a piece of work. Working alone, A could have completed the same work in 190 hours. B could have completed the same work in 285 hours, while C could have completed it in 342hours.The trio decided that one of the three would work at any point of time. In the first cycle of three days A worked for two hours on Day 1, B worked two hours on Day 2, and C worked for two hours on Day 3. In the second cycle of three days A worked for four hours on Day 1, B worked for four hours Day 2, and C worked for four hours on Day 3.In the third cycle of three days A worked for six hours on Day 1, B worked for six hours on Day 2, and C worked for six hours on Day 3. This continued till the piece of work was completed. with each working for 2n hours in Cycle n, the sole exception  being made, if necessary, in the Last cycle, as the work may get completed mid—cycle. What was the total number of days needed for the work to completed ?