Question

# 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.

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Solution

## 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=x+82[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−x2+544−8x⇒x2+75x−60x−544=0⇒x2+15x−544=0⇒x2+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=17So, 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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