Explanation:

If A and B can do a piece of work in x days, B and C in y days, C and A in z days, then (A + B + C) working together will do the same work in
[2xyz /xy + yz + zx] days
Given:
A and B together finish a piece work = x = 20 days
B and C together finish a piece work = y = 10 days
C and A together finish a piece work = z = 12 days
By the short trick approach:
A, B and C can do the work in
= 2 × 20 × 10 × 12 /20 × 10 + 10 × 12 + 12 × 20 days
After taking 40 as a common term we get,
= 10 x 12 /5 + 3 + 6 days = 120/14 = 8 4/7 days