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
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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, 4more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.
November 22, 2019avatar
Ajeeta Rai
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ANSWER
Let x be the number of days in which 150 workers finish the work.
According to the given information,
150x=150+146+142+...(x+8)terms
The series 150+146+142+...+(x+8) terms is an A.P. with first term 150, common difference -4 and number of terms as (x+8)
⇒150x=
2
x+8
[2(150)+(x+8−1)(−4)]
⇒150x=(x+8)[(150)+(x+7)(−2)]
⇒150x=(x+8)(150−2x−14)
⇒150x=(x+8)(136−2x)
⇒75x=(x+8)(68−x)
⇒75x=68x−x
2
+544−8x
⇒x
2
+75x−60x−544=0
⇒x
2
+15x−544=0
⇒x
2
+32x−17x−544=0
⇒x+(x+32)−17(x+32)=0
⇒(x−17)(x+32)=0
⇒x=17 or x=−32
Since, x cannot be negative . So, x=17
So, the number of days in which the work was to be completed by 150 workers is 17.
So, required number of days =(17+8)=25
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