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  • 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on.

32.  150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on.

Answers (1)

best_answer

Let x be the number of days in which 150 workers finish the work.

According to the given information, we have 

150x=150+146+142+............(x+8)terms

Series 150x=150+146+142+............(x+8)terms  is a AP

first term=a=150

common difference= -4

number of terms = x+8

\Rightarrow 150x=\frac{x+8}{2}\left [ 2(150)+(x+8-1)(-4) \right ]

\Rightarrow 300x=x+8\left [ 300-4x-28 \right ]

\Rightarrow 300x= 300x-4x^2-28x+2400-32x+224

\Rightarrow x^2+15x-544=0

\Rightarrow x^2+32x-17x-544=0

\Rightarrow x(x+32)-17(x+32)=0

\Rightarrow (x+32)(x-17)=0

\Rightarrow x=-32,17

Since x cannot be negative so x=17.

Thus, in 17 days 150 workers finish the work.

Thus, the required number of days = 17+8=25 days.

Posted by

seema garhwal

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