P works twice as fast as Q. Q alone can complete some work in 12 days. Working together, how long will P and Q take to complete the work?

P works twice as fast as Q

let q's effi = x

p's eff = 2x

Q = 12 days

as we know work = $$effi\times days$$  (we have the effi and days  of Q)

                          = $$x\times 12$$

                            = 12x

so P time taken = $$work\div effis$$

                           = 6 days

total effi = x + 2x = 3x

total time taken =$$12x\div 3x$$

                               = 4 days