Question

20 men can do a piece of work in 15 days. if 10 men leave the group after 10 days how many more days will the rest of the workers take ?


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Answer 1

Answer:

Twenty men can complete a work in 15 days. It means that the work requires 20*15 = 300 man-days. The first day there was 1 man, and next day another man joined and so on, each day 1 man was added, it went on till the work was completed. How many days did the work take for completion. The problem is an AP, with a = 1 and d=1, so we have

300 = (n/2)[2*1 +(n-1)*1], or

600 = n[2 +n - 1], or

600 = n(n+1), or

n^2 + n - 600=0

(n+25)(n-24)=0

So it will take 24 days to complete the work.

Check: S25 = (24/2)[2*1 + (24–1)*1] = (24/2)[2+23] = 24*25/2 = 300. Correct.

So it will take 24 days to complete the work.

Step-by-step explanation:

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