Question

A and b do a work with 5 days, a and c in 6 days, b and c in 20 days.if a do alone how many days it will take?

Answer 1

Let A, B and C do the job alone in A , B and C number of days.
Productivity per day of A, B and C =  1/A, 1/B and 1/C respectively.

1/A + 1/B = 1/5     ---(1)
1/A + 1/C = 1/6   --- (2)
1/B + 1/C = 1/20   --- (3)

(2) - (3) =>  1/A - 1/B = 7/60
Add (1) to get:   1/A = 19/120      So  A = 120/19 days