80 men can do a work in 40 days. After how many days should 20 men lea

1.	80 men can do a work in 40 days. After how many days should 20 men leave so that the whole work is completed in 50 days?
Answer» In 40 days 80 men do whole work Let after n days 2o men leave and remaining (80-20)=60men complete the work in (50-n)days So in n day 80 men will do n/40 part of whole work And in (50-n )days 60 men will do (50-n)×60/40×80) =(50-n)×3/160part work Hence n/40+(50-n)×3/160=1 =>4n+150-3n=160 =>n=10 Let after p days 20 men left Let w work done by 80 men in p days therefore, (80 x 40)/1 = (80 x p)/w w = p/40 remaining work = 1 - p/40 = (40 - p)/40 Now, 20 men leave after p days therefore, (80 x 40)/1 = 60(50 - p)/[(40 - p)/40] p = 10

80 men can do a work in 40 days. After how many days should 20 men leave so that the whole work is completed in 50 days?

Answer» In 40 days 80 men do whole work

Let after n days 2o men leave and remaining (80-20)=60men complete the work in (50-n)days

So in n day 80 men will do n/40 part of whole work

And in (50-n )days 60 men will do (50-n)×60/40×80) =(50-n)×3/160part work

Hence

n/40+(50-n)×3/160=1

=>4n+150-3n=160

=>n=10

Let after p days 20 men left

Let w work done by 80 men in p days

therefore,

(80 x 40)/1 = (80 x p)/w

w = p/40

remaining work = 1 - p/40

= (40 - p)/40

Now,

20 men leave after p days

therefore,

(80 x 40)/1 = 60(50 - p)/[(40 - p)/40]

p = 10

Discussion

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