Correct Answer: 42 days

Solution :

Given: Number of days P and Q take to do a piece of work = 14 days
Number of days Q and R take to do a work = 21 days
P is twice as good as Workman as R
Let P, Q, and R can do the work in $x, y$, and $z$ days respectively.
Let the amount of work done by P, Q, and R in 1 day is $\frac{1}{x},\frac{1}{y}$, and $\frac{1}{z}$ respectively.
According to the question,
$\frac{1}{x}+\frac{1}{y}=\frac{1}{14}$...................... (1)
$\frac{1}{y}+\frac{1}{z}=\frac{1}{21}$...................... (2)
As per the condition given, $\frac{1}{x}=\frac{2}{z}$
Putting the value in equation (1), and subtracting equation (2) from (1), we get
⇒ $\frac{2}{z}+\frac{1}{y}-\frac{1}{z}-\frac{1}{y}=\frac{1}{14}-\frac{1}{21}$
⇒ $\frac{1}{z}=\frac{3-2}{42}$
⇒ $z$ = 42 days
Putting the value of z in equation (2), we get:
⇒ $\frac{1}{y}=\frac{1}{21}-\frac{1}{42}$
⇒ $\frac{1}{y}=\frac{2-1}{42}$
⇒ $y$ = 42 days
Hence, the correct answer is 42 days.