A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?

The correct answer is: 30 days.

Let’s say the total work is represented as W and let’s say the work done by A in 1 day is W_A, work done by B in 1 day is W_B and work done by C in 1 day is W_C
Step 1 of 3:
It is given that A and B can do a piece of work in 18 days. So we can write
W_A  12 + W_B  12 = W
W_A  + W_B = …….(1)
It is given that B and C  can do a piece of work in 24 days. So we can write
W_B  15 + W_C  15 = W
W_B + W_C = …….(2)
It is given that A and C  can do a piece of work in 36 days. So we can write
W_A  20 + W_C  20 = W    …….(3)
W_A + W_C = …….(3)
Step 2 of 3:
Now, adding equations (1), (2) and (3)
2(W_A  + W_B + W_C )=  +  + 
W_A  + (W_B + W_C ) =   
Putting the value of W_B + W_C from equation (2)
W_A  +  =   = 
W_A  =  
Step 3 of 3:
Now, we can say that time taken by A to complete  amount of work = 1 day
So, the time taken by A to complete W amount of work =  = 30 days
Final Answer:
Hence, the time that will A alone take to finish the work is 30 days.