12 men working 8 hours a day can complete the work in 4 days
12 men working
1 hour a day will complete the same work in (8 x 4) days [
working less hours a day means they have to work for more days]
1 man working 1 hour a day will complete same work in (8 x 4 x 12) days [
fewer number of men working means the remaining ones will have to work for more days ]
So, it will take
1 man working
1 hour a day to complete a piece of work in
(8 x 4 x 12) days = 384 daysNow,
1 man working
16 hours a day will complete the piece of work in (384/16) days = 24 days [
working more hours a day means less days to complete the work]
∴
4 men working 16 hours a day will complete the piece of work in (24/4) days = 6 days [
more men working means fewer days to complete the work]
ALTERNATIVELY
12 x 8 x 4 = 4 x 16 x d
⇒ d = 4×1612×8×4
⇒ d = 64384
⇒ d = 6
∴ 4 men working 16 hours a day will complete the piece of work in 6 days