P and Q can do a piece of work in 14 days. Q and R together can do it in 21 days. If P is twice as good a workman as R, then in how many days Q alone can do the work?

42 days

P + Q = 14 days,

Q + R = 21 days,

As Given, 

P is twice efficient than R, therefore

⇒ P : R = 2 : 1 (Efficiency)

⇒ P + Q = 3,  Q + R = 2, 

Solving the efficiencies we get all the efficiencies, i.e;

P = 2, Q = 1, R = 1,

⇒ Time taken by Q to complete total work alone = \(\frac{42}{1}\) = 42 days.  ..(\(\frac{Work}{Efficiency}\) = Time )