12 men dig a trench

Question

12 men dig a trench in 18days. How long should it take 9 men?

Answer 1

The work in man-days (now, person-days) is the about of effort required to dig the trench.  This trench takes 18*12 = 216 man-days to dig.   And, at $300/man-day (for example) you could calculate the cost of digging the trench.

Now, 9 men will take longer.  They will take 216 man-days / 9 men  = 24 days.    (note: getting the units straight is important here).

Simply,

      12*18 = 9*x

 

Answer 2

Simple ratio

 

12/18 = 9/x

 

2/3= 9/x

 

2x = 27

 

x = 13 1/2

Answer 3

12     9

18 = x

 

cross-multiply

 

12x = 18(9)

 

12x = 162

 

divide each side by 12

 

x = 162/12

 

x = 13.5

 

It should take 9 men 13.5 days to dig the trench.