P can complete a work in 12 days working 8 hours a day, Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

P's rate: P completes the work in 96 hours (12 days × 8 hours/day). So, P’s work rate is 1/96 of the work per hour. Q's rate: Q completes the work in 80 hours (8 days × 10 hours/day). So, Q’s work rate is 1/80 of the work per hour. When they work together, their combined work rate is:

Thus, together they complete 11/480 of the work per hour. The time taken to complete the work is:

Since they work 8 hours a day, the number of days they will take is:

or  5(5/11)