Explanation:

Correct option 2: 29/3 days

Given:
X can complete a piece of work in = 16 days
Y can complete a piece of work in = 24 days
Work starting alternatively with Y.
Calculation:
Total Work = LCM(16,24)
= 48 units
:: 50% work = 48/2 = 24 units
Efficiency of X = 48/16 = 3 units/day
Efficiency of Y = 48/24 = 2 units/day
.. 2 days work of X and Y = 3 + 2 = 5 units
.. If they work together, they can complete work in 8 days = 4 x 5 = 20 units
On the 9th day, y works, so total work completed till 9th day = 20 + 2 = 22 units Work remaining = 24 - 22 = 2 units
On the 10th day, x works, efficiency of x = 3 units
so (2/3) part of the 10th day, the work will be completed.
Total days required = 9 + 2/3 = 29/3
:: The required days to complete 50% of the work are 29/3.