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 P and Q work together, working 8 hours a day, in how many days can they complete the work?

Explanation:

P can complete a work in 12 days working 8 hours a day

∴ P can complete a work in 12 days working 1 hours a day = 1\8

∴ P’s 1 day work working 1 hour a day = 1\8×12

Similarly, Q’s 1 day work working 1 hour a day

∴ (P + Q)’s 1 day work working 1 hour a day

= 1\8×12+1\8×10

= 5+6\60×8 = 11\60×8

∴ (P + Q)’s 1 day work working 8 hours a day

= 11×8\60×8 = 11\60

∴ No of days required

= 5 5\11days.