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Bunuel
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Bunuel
A group of 20 software engineers can finish a development project in 30 days. They got a project with the deadline of 35 days. After how many days should 5 engineers be released so that the project completes on time?

(A) 5
(B) 8
(C) 10
(D) 12
(E) 15
The total time is 35 days and the total workers is 20. Say for the first t days, all 20 workers will work. Finally, for (35-t) days, only (20-5)=15 people will work.
Let us calculate the individual rate first.

20 workers' 1-day work (i.e. Rate) = 1/30 work/day
1 worker's 1-day work (i.e. Rate) = 1/600 work/day
15 workers' 1-day work (i.e. Rate) = 15/600 = 1/40 work/day

We know, Rate*Time = Work

t*(1/30) + (35-t)*(1/40) = 1
or, t/30 + (35-t)/40 = 1
Upon solving, we will get t=120-105=15 days, i.e. after 15 days, only 15 workers will work. Option (E) is correct.
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Existing total Mandays 20*30 = 600

Project days extended to 35 days, New Mandays = 20*35 = 700

Excess mandays avaialble = 700-600 = 100

Total 5 people to be released 100 mandays/5 = 20 days

No of days engineers can be release 35-20 = 15 days
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