Latest CAT Aptitude Question SOLUTION: a contractor agreed to complete a work in 40 days.he engaged 25 men for the work and after 24 days,only one third of the work was completed.how many more men must he employ to comp

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(#M40038429) CAT Category question ss Keep an EYE

a contractor agreed to complete a work in 40 days.he engaged 25 men for the work and after 24 days,only one third of the work was completed.how many more men must he employ to complete the work 4days earlier?

Asked In CAT MohanRaj (10 years ago)

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nandhakumar  (10 years ago)

25 men work in 24 days,and 1/3rd of work,
remaining work= 1-1/3= 2/3
4 days earlier =40-4=36,
remaining days to work=36-24=12
so , 12 men 2/3rd of work = (25*24*1/3) /(12*2/3)=100

already 25 men worked, so added men is= 100-25=75

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ATUL TRIPATHI  (10 years ago)

24*25=w/3
w=24*25*3=1800 mandays
work done=25*24=600 mandays
remaining work= 1800-600= 1200 mandays
and d work to be doing in 12 days so
1200/12= 100 men will be required
out of which 25 are already working
so 100-25= 75 men more will be required

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Devendra Marghade  (10 years ago)

75 men

25 men's, 24 day work= 1/3
25 men's, 1 day work= 1/(3*24)
1 man's, 1 day work= 1/(3*24*25)
Work remaining= 2/3 and is to be completed in total 40-4=36 days
As already 24 days are over, so if 'x' more men are employed, then, existing 25 men & extra 'x' men should work for 36-24= 12 days.
12/(3*24) + 12*x/(3*24*25) =2/3
On solving, x=75

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SUDHIR SHARMA  (10 years ago)

Work done by 25 men for 24 days = 25*24 men-days = 1200 men-days
It is given that only 1/3rd work was done.

Therefore, 33.33% work = 600 men-days
or 1% work = 600/33.33 men-days

Remaining work = 100-33.33 = 66.67

so, 66.67% work = 1200*66.67/33.33 = 1200 men-days

The work has to be completed before 4 days.
It means 40-24-4 = 12 days are remaining to compete the work.

1200 men-days = 100men * 12 days

and 100-25 = 75 (because 25 men we already have)

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Chirag Ranjan Lahiri  (10 years ago)

w=24*25*3=1800 mandays
work done=25*24=600 mandays
remaining work= 1800-600= 1200 mandays
and d work to be doing in 12 days so
1200/12= 100 men will be required
out of which 25 are already working
so 100-25= 75 men more will be required

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