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