Question

# 150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped the second day, four more workers dropped the third day and so-on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed.

A
24 days
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B
25 days
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C
26 days
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D
27 days
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Solution

## The correct option is C 25 daysLet the work can be completed in 'n' daysAccording to question4 worker dropped out everyday except the first day.Now, Total number of worker who work on n days is the sum of 'n' term of A.P. whose 1st term = 158common difference = -4∴ Total number of worker who work on n days⇒n2[2×150(n−1)(−4)⇒n(152−2n)If 150 workers work on everyday then the work will be completed in (n−8) days∴ Total no of worker who work on n days =150(n−8)∴n(152−2n)=150(n−8)⇒152n−2n2=150n−1200⇒2n2−2n−1200=0⇒n2−n−600=0⇒n2−25n+24n−600=0⇒n(n−25)+24(n−25)=0⇒(n−25)(n+24)=0∴n=25 or n=−24Taking positive terms n=25 So, the work will be completed in 25 days.

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