Option 2 : \(27{19\over29}\) days

**Given:**

A complete work = 81 days

B complete work = 54 days

C complete work = 72 days

**Formula used:**

Efficiency = Total work/Time

**Calculation:**

Let the total work be L.C.M of 81, 54 and 72

⇒ Total work = 648 units

Efficiency of A, B and C = 8, 12 and 9, respectively

∵ A left 8 days before the work was completed and C left 10 days before the work was completed.

So, for the last 8 days, only B is working

⇒ Work done by B = 12 × 8 = 96 units

For the 2 days, only A and B were working

⇒ Work done by A and B = (12 + 8) × 2 = 40 units

So, the remaining work

⇒ 648 - 96 - 40 = 512

Time taken to complete remaining work

⇒ 512/29 = \(17{19\over29}\)

Total time taken to total work done

⇒ \(17{19\over29}\) + 2 + 8

⇒ \(27{19\over29}\) days

**∴ Total time taken to total work done is **\(27{19\over29}\)** days.**