If 9 Men built 8 cabinets in 12 days, How many cabinets can 6 men build in 4 days?

Question

If 9 Men built 8 cabinets in 12 days, How many cabinets can 6 men build in 4 days?

Answer 1

To build 8 cabinets it took (9 men) (12 days) = 108 man-days

To build 1 cabinet it takes 27/2 man- days

The rate for building a cabinet is 2/27 cabinet/man-days.

 

6 men working for 4 days is 24 man-days

They can build (2/27  cabinet/man-days) (24 man-days) =  16/9 ≈ 1.8 cabinets.

Answer 2

There are 2/3 of the men, and 1/3 the days.

Therefore only 2/9 (2/3 · 1/3) of the cabinets are made

(2/6)(8) = 1.777

So only one cabinet.

 

If you want algebra:

 

8 cabinets : 108 mandays :: c cabinets : 24 mandays

108c = 192

c = 1.777 

 

Only one cabinet is made.