150 workers were engaged to finish a job in a Certain number of days. 4 workers dropped number of day, 4 more workers drop on third day so on. It took 8 more days to finish the work find the number pf days in which the work was completed.
Please help me
Answers
Step-by-step explanation:
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
Answer:
answer is 25 days
Step-by-step explanation:
suppose the work is completed in n days
since four workers went away on every day except the first day
: total number of worker who worked all the n days is the sum of n terms of A.P . with first term 150 and common difference –4.
total number of worker who worked all the n days
= n/2 [2×150 + (n–1) × (–4)]
= n(152–2n)
if the workers would not have went away, then the work would have finished in (n–8) days with 150 workers working on every day
: total number of workers who would have worked all n days= 150(n–8)
n(152–2n) = 150(n–8)
152n–2n²= 150n–1200
2n²–2n–1200=0
n²–n–600 = 0
n²–25n+24n–600=0
n(n–25) +24 (n+25) =0
(n–25) (n+24) =0
n–25= 0 (or) n+24= 0
n= 25 (or) n=–24
n=25 ( : number of days cannot be negative)
thus, the work is completed in 25 days
I hope you understand friend