A and B can polish the floors of a building in 10 days. A alone can do ¼th of it in 12 days. In how many days can B alone polish the floor?

The correct answer is: 12 12/19 days

Let’s say that the total area of the floors to be polished is A and let’s say that person A can polish an area of A_A in 1 day and person B can polish an area of A_B in 1 day.
Step 1 of 3:
It is given that person A alone can polish an area of A/4 in 12 days.
So, Area polished by person A in one day(A_A) =  = …….(1)
Step 2 of 3:
It is given that person A and person B can polish the floors of a building in 10 days. So we can write
A_A 10 + A_B  10 = A
Using equation (1)
10 + A_B 10 = A
A_B =  A
Step 3 of 3:
Now, the time taken by person B to polish an area A = 1 day
So, time taken by person B to polish an area A = A =  days =  days
Final Answer:
Hence, the time that will person B alone take to polish the floor is  days.