A can do a piece of work in 6 days working 8 hours a day. B can do the same work in 4 days working 6 hours a day. If they work together 8 hours a day, in how many days they will do this work?

Question: A can do a piece of work in 6 days working 8 hours a day. B can do the same work in 4 days working 6 hours a day. If they work together 8 hours a day, in how many days they will do this work?

Solution:
A can complete the work in, 6 × 8 = 48 hour
B can complete the same work in = 4 × 6 = 24 hours

A's one hour work = 1/48
B's one hour work = 1/24
(A +B)'s one hour work = 1/48 + 1/24 = (1 + 2)/48 = 3/48 = 1/16

They will complete 1/16 of work in 1 hour
So, the entire work will be completed in 16 hour

Both work 8 hours a day so the number of days required to complete the work = 16/8 = 2 days