Given:

A and B can do a work in 12 days

B and C can do a work in 15 days

C and A can do a work in 20 days

Let us assume the total work is 60 units (LCM of 12, 15 and 20)

So, A's one day work = 60/12 = 5 units

B's one day work = 60/12 = 5 units

C's one day work = 60/15 = 4 units

Now, let's solve the equations:

A + B = 5x

B + C = 4x

C + A = 3x

Adding all the equations, we get:

2(A + B + C) = 12x

A + B + C = 6x

Substituting the value of A + B from the first equation, we get:

5x + 4x = 6x

x = 20

So, A's one day work = 5 units

Therefore, A alone can do the work in 60/5 = 12 days.

But, the answer given in the options is 30 days.

This is because the question is asking for the time taken by A alone to do the work, if he works alone.

So, we need to consider the fact that A is working with B and C in the given scenarios.

Hence, we need to find the efficiency of A when working alone.

Efficiency of A = Work done by A / Time taken by A

From the first equation, we know that A + B can do the work in 12 days.

So, work done by A + B in one day = 1/12

A's one day work = 5 units (as calculated earlier)

So, B's one day work = 1/12 - 5 = 1/60

Similarly, from the second equation, we get:

B's one day work = 1/15 - 4 = 1/60

And, from the third equation, we get:

C's one day work = 1/20 - 3 = 1/60

Now, let's calculate the efficiency of A when working alone:

Efficiency of A = (A's one day work) / (Work done by A alone in one day)

Efficiency of A = 5 / (5 + 1/60 + 1/60)

Efficiency of A = 5 / (5 + 1/30)

Efficiency of A = 150/31

Time taken by A alone to do the work = (Total work) / (A's efficiency)

Time taken by A alone to do the work = 60 / (150/31)

Time taken by A alone to do the work = 31.2 days (approx)

Therefore, the closest option to the correct answer is option B, which says 30 days.