A does 50% of a work in 12 days. He then calls in B and they together finish the remaining work in 8 days. How long B alone would take to complete the whole work?

A completes 50% (or
2
1
​
) of the work in 12 days.
Therefore, A can complete the whole work alone in:

12×2=24 days
So, A's 1-day work rate =
24
1
​


The remaining work is 100%−50%=50% (or
2
1
​
).
A and B together finish this remaining
2
1
​
work in 8 days.
Therefore, A and B together can complete the whole work in:

8×2=16 days
So, (A + B)'s 1-day work rate =
16
1
​


Now, B's 1-day work rate can be found by subtracting A's rate from their combined rate:

B’s 1-day work=
16
1
​
−
24
1
​

Taking the LCM of 16 and 24, which is 48:

B’s 1-day work=
48
3−2
​
=
48
1
​

Thus, B alone would take 48 days to complete the whole work.