Question

150 workers were engaged to finish a piece of work in a certain period of days for workers dropped by second day 4 workers drop the third day and so one it takes 8 more days to finish the work now find the number of days in which the work was completed​

Answer 1

Answer

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

n days. Therefore,

total work =150+146+... (n terms)

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

total work=

2

n

[2×150+(n−1)(−4)]

=

2

n

[304−4n]

=n(152−2n)_____^^(2)

from (1) and (2),

150(n−8)=n(152−2n)

75(n−8)=n(76−n)

n

2

−n−600=0

(n−25)(n+24)=0

∴n=25

Answer 2

Answer:

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Step-by-step explanation:

150 workers were engaged to finish a piece of work in a certain period of days for workers dropped by second day 4 workers drop the third day and so one it takes 8 more days to finish the work now find the number of days in which the work was completed