P can complete 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?

Question: P can complete 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?

Solution:
P can complete the work in (12 × 8) hrs = 96 hrs
Q can complete the work in (8 × 10) hrs = 80 hrs
Therefore, P's 1 hour work = 1/96 and Q's 1 hour work = 1/80

(P + Q)'s 1 hour's work = (1/96) + (1/80)
= 11/480

So both P and Q will finish the work in 480/11 hrs
Therefore, Number of days of 8 hours each = (480/11) × (1/8) = 60/11