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150 workers were engaged to finish a piece of work in a certain number of day. four worker added on the second day, four more workers added on third day

and so on. it takes 8 less days to finish the work now. find the number of days in which the work was completed

Let x be the number of days in which 150 workers finish the work. According to the given information, 150x = 150 + 146 + 142 + …. (x + 8) terms The series 150 + 146 + 142 + …. (x + 8) terms is an A.P. with first term 146, common difference –4 and number of terms as (x + 8)

However, x cannot be negative. ∴x = 17 Therefore, originally, the number of days in which the work was completed is 17. Thus, required number of days = (17 + 8) = 25

Let the work has been completed in n days total no. of workers = 150+146+142.... n/2 (150×2+(n-1)4) total no. of workers = 150 (n-8) n(150+2n-2)= 150 (n-8) 150n+2n×n-2n= 150n -150×8 n×n-n+600 n= 25