IMO, the answer is 9 days.

The good part is that we do not have to do full calculations. We can figure out that the work gets done on the 9th day (without having to figure out as to how many hours into the day or as to how many shifts into the day)

A finishes the job in 24 shifts. B finishes in 30 shifts.

Part of the job done per day = (1/24 + 1/30 + 1/48 + 1/60).

Small suggestion - Do not take LCM of 24, 30, 48 and 60. Just add 1/24 and 1/48 first. Add 1/30 and 1/60 next. You are left with 1 / 16 + 1 / 20 = 9 / 80.

At the end of the 8th day, 72 / 80 parts of the job are done. At the end of the 9th day, 81 / 80 parts of the job are done - implying that the work gets done a few hours before the day ends. But, it does not matter as far as the question is concerned.

Hope this helps.

While doing 2 shifts A takes 12 days to complete,
therefore while doing 1 shift hell take 24
or doing 1.5 shifts(amount done in one day) he takes 16

Similarly B working everyday 1.5 shifts will take 20 days.

Now

1/20 + 1/16 = 1/x

x = 8.88 = 9 days