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 will finish.

Answer 1

Ans: 25

Suppose 1 worker does 1 unit work in a day

Assume 150 workers can finish the work in (n-8) days, if all workers work all the days.
Then, total work =150(n−8) ⋯(1)

Actually 150 workers work on day-1, 146 workers work on day-2, ... and work is completed in nn days. Therefore,
total work =

150 + 146 + ... (nterms)

This is an arithmetic progression with a = 150, d = -4. Therefore,

total work
=n/2[2×150+(n−1)(−4)]

=n/2[300−4n+4]


=n/2[304−4n]

=n(152−2n) ⋯(2)



From(1) and (2)
150(n−8)=n(152−2n)

75(n−8)=n(76−n)

75n−600=76n−n^2

n^2−n−600=0

(n−25)(n+24)=0


n=25


i.e., number of days in which the work was completed = 25