Option 2 : 36 hours

__GIVEN:__

the efficiency of A = efficiency of B and C together

time taken by A and B to complete = 12 hours

time taken by C to complete = 36 hours

__CONCEPT:__

The time required to complete the work is the reciprocal of the fraction of work done in one time period (one hour).

__EXPLANATION:__

(A + B)'s one hour work = \(\frac{1}{12}\)

C's one hour work = \(\frac{1}{36}\)

(A + B + C)'s one hour work = \(\frac{1}{12}+\frac{1}{36}=\frac19\)

replace B + C with A as the efficiency of both is the same

(2A)'s one hour work = \(\frac19\)

A's one hour work = \(\frac{1}{18}\)

B's one hour work = \(\frac{1}{12}-\frac{1}{18}=\frac{1}{36}\)

∴ time taken by B to complete the whole work = 36 hours

__ __

Let total work = 36 (L.C.M of 12, 36)

(A + B)'s one hour work = 3

C's one hour work = 1

(A + B + C)'s one hour work = 4

replace B + C with A as the efficiency of both is the same

(2A)'s one hour work = 4

A's one hour work = 2

B's one hour work = 3 - 2 =1

∴ time taken by B to complete the whole work = \(\frac{36}{1}=36 hours\)