A and B can complete a piece of work in 13 and 17 days respectively. A begins to do the work, and they work alternatively one at a time for one day each. The whole work will be completed in:

$14 \frac{11}{17}$ days

A = 13 days, B = 17 days,

Since A and b are working on alternate days starting with A, 

1st day work (A) =      17 units

2nd day work (B) =     13 units

Every 2 days of work =30 units

⇒ So, in 14 days, 210 units of work will be completed,

⇒ The remaining work i.e; 11 units will be completed by A in \(\frac{11}{17}\) days.

⇒ Therefore, Total taken to complete the work = 7 + \(\frac{11}{17}\) = \( {7 }_{17 }^{ 11} \) days.