Explanation

A and B can do the work in 12 days, so their combined rate of work is 1/12 of the work per day.

B and C can do the work in 15 days, so their combined rate of work is 1/15 of the work per day.

C and A can do the work in 20 days, so their combined rate of work is 1/20 of the work per day.

Now, let's add the three equations and simplify:

2(A + B + C) = 1/12 + 1/15 + 1/20

Combine like terms:

2(A + B + C) = (10 + 8 + 6) / 120

Simplify the fraction:

2(A + B + C) = 24 / 120

Divide both sides by 2:

A + B + C = 12 / 120

Simplify the fraction:

A + B + C = 1/10

So, A, B, and C together can complete 1/10 of the work in one day.

To find the number of days taken by A, B, and C together to finish the work, we take the reciprocal:

Number of days = 1 / (1/10) = 10 days