If 3 men or 9 boys can finish a piece of work in 21 days, in how many days can 5 men and 6 boys together do the same piece of work ?

A. 8 days

B. 12 days

C. 14 days

D. Cannot be determined

E. None of these

Answer: Option E

Solution(By Examveda Team)

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{21 \times 3}} \cr & = \frac{1}{{63}} \cr & {\text{1 boy's 1 day's work}} \cr & = \frac{1}{{21 \times 9}} \cr & = \frac{1}{{189}} \cr & \left( {{\text{5 men}} + {\text{6 boy}}} \right){\text{'s 1 day's work}} \cr & = \frac{5}{{63}} + \frac{6}{{189}} \cr & = \frac{5}{{63}} + \frac{2}{{63}} \cr & = \frac{7}{{63}} \cr & = \frac{1}{9} \cr} $$
Hence, 5 men's and 6 boy's together can do the work in 9 days.