X alone can complete a piece of work in 16 days, while Y alone can complete the same work in 24 days. They work on alternate days starting with Y. In how many days will 50% of the total work be completed?

$\frac{29}{3}$ days

X = 16 days, Y = 24 days,

⇒ They work on alternate days, starting with Y,

 1st day = 2 units,

 2nd day = 3 units,

Every 2 days = 5 units of work is done,

So, in 8 days, 20 units of work will be completed,

And in 9 days, 22 units will be completed,

Therefore, in \( { 9}_{3 }^{2 } \) = \(\frac{29}{3}\) days, 50% of the work will be completed.