8 men can complete a piece of work in 20 days. 8 women can complete the same work in 32 days. In how many days will 5 men and 8 women together complete the same work ?

A. 10 days

B. 12 days

C. 14 days

D. 16 days

E. None of these

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{20 \times 8}} \cr & = \frac{1}{{160}} \cr & {\text{1 women's 1 day's work}} \cr & = \frac{1}{{32 \times 8}} \cr & = \frac{1}{{256}} \cr & \left( {{\text{5 men}} + {\text{8 women}}} \right){\text{'s 1 day's work}} \cr & = \frac{5}{{160}} + \frac{8}{{256}} \cr & = \frac{1}{{32}} + \frac{1}{{32}} \cr & = \frac{1}{{16}} \cr} $$
Hence, 5 mens and 8 women together can complete the work in 16 days.