One man and one woman can complete a piece of work in 18 days while four men and three women can complete the same work in 5 days. In how many days can two men and three women complete the same work?

Let the efficiency of a single man and single woman by M units/day and W units/day respectively. 

The first statement is : Total work = 18(M + W)                       {Work = Time x efficiency}
The second statement is: Total work = 5(4M  + 3w)

Since, the total work is same in both the equations, we can equate them to get;
$$18M+18W=20M+15W$$
$$3W=2M$$
$$M=\frac{3}{2}W$$

With this relation, we can find the total work in terms of W or M; Using equation 1 to find the total work in terms of W we get, 
$$18\left(\frac{3}{2}W\right)+18W=45W$$
Now the time taken by 2 men and 3 women to do this work will be 
Time x($$2\left(\frac{3}{2}W\right)+3W\ =\ 45W$$
Time = $$\frac{45}{6}=\frac{15}{2}=7\ \frac{1}{2}$$

Therefore, Option B is the correct answer.