A and B working separately can finish a work in 18 days and 24 days, respectively. A begins the work and works for two consecutive days, while B works on the 3rd day. This pattern is continued till the work is completed. In how many days will the work be completed?

Correct option is D

Given:
A works in 18 days and B works in 24 days
Solution:

Efficiency of A and B are 4 and 3 respectively
Work done by A in 2 days = $$2 \times 4 = 8 units$$ 
Now on 3rd Day, B both will work = 3 unit of work will be completed on 3rd day
Similarly pattern goes on, 
So, In total 3 days = 11 unit of work completed
In next 3$$\times 6 = 11 \times 6$$ unit of work completed
​In next 18 days = 66 unit of work completed
Remaining work = 72- 66 = 6 unit 
6 unit of work will be completed by A in $$\frac{6}{4} = \frac{3}2 = 1 \frac 12 \text {days}$$ 
Total Time = 19 $$\frac 12$$ days​