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Question

150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

A
15
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B
20
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C
25
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D
30
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Solution

The correct option is C 25
Suppose 1 worker does 1 unit work in a day

Assume 150 workers can finish the work in (n8) days, if all workers work all the days.
Then, total work
=150(n8)⋯(1)

Actually 150 workers work on day-1, 146 workers work on day-2, ... and work is completed in
n days. Therefore,
total work =150+146+... (n terms)

This is an arithmetic progression with a=150, d=4. Therefore,
total work=n2[2×150+(n1)(4)]

=n2[3044n]

=n(1522n)............(2)

from (1) and (2),

150(n8)=n(1522n)

75(n8)=n(76n)

n2n600=0

(n25)(n+24)=0

n=25

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