Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q, and R together can complete the work in 30 days, then in how many days P alone can do the work?

Let P's work per day = $x$ units

Then Q's work per day = $\frac{x}{2}$ units

And R's work per day = $\frac{x}{6}$ units

Total work per day by all three = $x + \frac{x}{2} + \frac{x}{6}$

$= \frac{6x + 3x + x}{6}$

$= \frac{10x}{6}$ units per day

If total work = $1$ unit and time taken = $30$ days

$\frac{10x}{6} \times 30 = 1$

$10x = \frac{6}{30}$

$x = \frac{6}{300} = \frac{1}{50}$

Therefore, P can do $\frac{1}{50}$ unit work per day

So P alone will take $50$ days to complete the work.