6 men can complete a piece of work in 64 days. 24 females can complete the same work in 32 days. 16 males and 24 females started the same work and after 12 days, 8 men and 8 women left the work, then find out the number of days taken to complete the total work.

Given,

6 men can complete the work in 64 days.

24 females can complete the work in 32 days.

Using Formula : $$\frac{M_1D_1E_1}{W_1}=\frac{M_2D_2E_2}{W_2}$$

where, M = number of persons

D = number of days to complete the work 

E = efficiency of working person

$$6  men\times\ 64=24 women\times\ 32$$

By solving ,we get 

 $$\frac{men}{women}=\frac{2}{1}$$

efficiency of men : 2

efficiency of women : 1

Total work = $$6\times\ 2\times\ 64\ =\ 768\ units $$

According to question, 

16 men and 24 women worked for 12 days

$$\left(\left(16\times\ 2\right)+\left(24\times\ 1\right)\right)\times\ 12=\ 672\ units$$

Remaining work = 768 - 672 = 96 units

but now 8 women and 8 men left the work, so remaining work is completed by remaining men and women

$$\frac{96}{\left(8\times\ 2\right)+16}=\frac{96}{32}=3\ days$$

the Number of days taken to complete the total work = 12 + 3 = 15 days

Hence, Option D is correct.