A twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is:

Let's denote the amount of work done by A in one day as "x" and the amount of work done by B in one day as "y."

According to the given information, A is twice as good a workman as B. This means that A can do twice the amount of work in a day as B. So, we can write:

x = 2y

Now, let's consider their combined work rate. Together, A and B can finish a piece of work in 14 days. Therefore, their combined work rate is:

(x + y) = 1/14

We already know that x = 2y, so we can substitute this into the equation:

(2y + y) = 1/14

Now, combine the terms on the left side:

3y = 1/14

To find y, the work rate of B in one day, divide both sides by 3:

y = (1/14) / 3 y = 1/42

Now that we know the work rate of B, we can find the work rate of A by using the relationship x = 2y:

x = 2 * (1/42) x = 2/42 x = 1/21

Now, we have found that A can complete 1/21 of the work in one day. To find out how many days A alone would take to finish the work, take the reciprocal of A's work rate:

Number of days taken by A alone = 1 / (1/21) = 21

So, A alone would take 21 days to finish the work.