The correct option is
C 25Suppose 1 worker does 1 unit work in a day
Assume 300 workers can finish the work in (n−8) days, if all workers work all the days.
∴ total work =300(n−8)..........(1)
According to question, 300 workers work on day 1, 292 workers work on day 2, ... and work is completed in n days.
∴ total work =300+292+...(n terms)
This is an arithmetic progression with a=300,&d=−8.
∴ total work =n2[2×300+(n−1)(−8)]
=n2[600−8n+8]
=n2[608−8n]
=n(304−4n)...(2)
From (1)&(2), we have
300(n−8)=n(304−4n)
75(n−8)=n(76−n)
75n−600=76n−n2
n2−n−600=0
(n−25)(n+24)=0
n=25
Hence, number of days in which the work was completed = 25.