A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

The correct answer is: 8 hours.

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 andwork 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  18 + W_B  18 = 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  24 + W_C  24 = 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  36 + W_C  36 = W
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 =   ……(4)
Step 3 of 3:
Let’s say the time taken by all of them to complete the work is t. So we can write
W_A  t + W_B  t + W_C  t = W
t(W_A  + W_B + W_C) = W
Using equation (4)
t   = W
t = 16 days
Final Answer:
Hence, the time taken by all of them to complete the work is 8 hours.