A, B and C can do some work in 40 days. A and C together can do twice as much work as B alone. Find the time taken by B to do the whole work.

When solving work problems, work rate represents how much work someone completes in 1 day. If someone finishes work in 10 days, their work rate is $\frac{1}{10}$ per day.

Work rate $= \frac{1}{\text{Time taken to complete whole work}}$

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Let $b$ = B's work rate (portion of work B does in 1 day)

Let $a$ = A's work rate (portion of work A does in 1 day)

Let $c$ = C's work rate (portion of work C does in 1 day)

Given that A, B, and C together finish the work in 40 days, their combined work rate is $\frac{1}{40}$ of the work per day.

$a + b + c = \frac{1}{40}$

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Given that A and C together can do twice as much work as B alone:

$a + c = 2b$

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Substituting $a + c = 2b$ into the first equation:

$2b + b = \frac{1}{40}$

$3b = \frac{1}{40}$

$b = \frac{1}{120}$

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If B's work rate is $\frac{1}{120}$ per day, then B completes the whole work in 120 days.

Therefore, the answer is 120 days.