A, B and C can do a piece of work in 30, 20 and 10 days resp. A is assisted by B on one day and by C on the next day, alternatively. How long would the work take to finish?

\(9\frac{3}{8}\)

1st day work by (A + B)  = 2 + 3 = 5

2nd day work by (A + C) = 2 + 6 = 8

Two days work = 5 + 8 = 13

⇒  In 2 days total work done = 13 Units

⇒  In 8 days total work done = 52 Units

⇒ On 9th day (A + B) work = 5

Therefore,

⇒  In 9 days total work done = 57 Units

⇒ Last 3 Units work is to be done by (A+ C) with the efficiency of '8',

So, Total Time to finish the work = 9 +\(\frac{3}{8}\) = 9\(\frac{3}{8}\)