A takes twice as much time as B, and C take thrice as much time as B to finish a work. Working together, they can finish the work in 12 days. Find the number of days needed for A to do the work alone.

Let time taken by B = N
Then, time taken by A = 2N
and time taken by C = 3N
According to the question,
(1/N) + (1/2N) + (1/3N) = 1/12
⇒ 1 + (1/2) + (1/3) = N/12
⇒ (6 + 3 + 2)/6 = N/12
⇒ 11 = N/2
∴ N = 22
∴ Required number of days = 2N = 2 x 22 = 44 days