16 men are employed to do a work in 20 days. at the end of 12 days the work is only half done. how many additional number of men should be employed to complete the work in the stipulated time?

16 men in 12 days can do 0.5work
1 man 1 day can do 0.5/(16x12) of a work

8days to do 0.5 of a work
1 man 8 days can do 8x0.5/(16x12) = 0.5x(1/24) of a work
... if you notice we need 24 men

... more detail
in8days, 0.5x(1/24) of a work need 1 man
in8days, 0.5 of a work need 0.5/(0.5x(1/24)) = 24 men

point is to find 'amount of work done per man per unit of time' then work out from that.