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Question

300 works were engeged to finish a piece of work in a certain number pf days. 8 workers dropped on the second day, 8 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
35
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B
30
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C
25
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D
28
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Solution

The correct option is C 25
Suppose 1 worker does 1 unit work in a day
Assume 300 workers can finish the work in (n8) days, if all workers work all the days.
total work =300(n8)..........(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+(n1)(8)]
=n2[6008n+8]
=n2[6088n]
=n(3044n)...(2)
From (1)&(2), we have
300(n8)=n(3044n)
75(n8)=n(76n)
75n600=76nn2
n2n600=0
(n25)(n+24)=0
n=25
Hence, number of days in which the work was completed = 25.

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