Explanation:

Let’s break it down:

- Let Q’s efficiency = x.

- Then, P’s efficiency = 2x.

- Work done by P + Q in 1 day: 2x + x = 3x.

- P + Q finish in 12 days: 3x × 12 = 36x (total work).

- Q + R’s 1 day work = x + y (let R’s efficiency = y).

- Q + R finish in 14 days: (x + y) × 14 = 36x ? x + y = 36x/14 ? y = (36x/14) - x ? y = 11x/7.

- R’s 1 day work is y/36x = (11x/7)/36x = 11/252.

- So, R alone finishes in 252/11 = 22 10/11 days.

Correct option:

Option 2: 22 10/11

Other options are incorrect because they do not match this calculation.