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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 was completed.

A
24 days
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B
25 days
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C
26 days
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D
27 days
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Solution

The correct option is C 25 days
Let the work can be completed in 'n' days

According to question

4 worker dropped out everyday except the first day.

Now,

Total number of worker who work on n days is the sum of 'n' term of A.P.

whose 1st term = 158

common difference = -4

Total number of worker who work on n days

n2[2×150(n1)(4)

n(1522n)

If 150 workers work on everyday then the work will be completed in (n8) days

Total no of worker who work on n days =150(n8)

n(1522n)=150(n8)

152n2n2=150n1200

2n22n1200=0

n2n600=0

n225n+24n600=0

n(n25)+24(n25)=0

(n25)(n+24)=0

n=25 or n=24

Taking positive terms

n=25

So, the work will be completed in 25 days.

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