It takes 12 men 8 hours a day to finish a piece of work in

Explanation

12 men working 8 hours a day can complete the work in 4 days

12 men working1 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 take1 man working1 hour a day to complete a piece of work in(8 x 4 x 12) days = 384 days

Now,

1 man working16 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 = \(\frac{12 \times 8 \times 4}{4 \times 16}\)

⇒ d = \(\frac{384}{64}\)

⇒ d = 6

∴ 4 men working 16 hours a day will complete the piece of work in 6 days