Question

$\sf \large \:\underline{ \red{Question }}:-$ 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. [Solve please please

Answer 1

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

hope this helps you ✌️

Answer 2

$\sf \large \:\underline{ \red{Question }}:-$

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.

$\sf \large \:\underline{ \red{Given} }:-$

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.

$\sf \large \:\underline{ \red{To \: Find }}:-$

Find the number pf days in which the work was completed.

$\sf \large \:\underline{ \red{Solution }}:-$

$\boxed{ \sf \: sum \: of \: n \: terms \: = \frac{n}{2} ( \:2a + (n - 1) \times d) }$

∴ Total number of workers who would have worked all n days = 150 (n – 8)

$\sf \to \: n (152 - 2n) = 150 (n - 8) \\ \\ </p><p></p><p> \sf \to \: 152n - 2n^2 = 150n - 1200 \\ \\ \sf \to \: 2n^2 - 2n - 1200 = 0 \\ \\ </p><p></p><p> \sf \to \: n^2 - n - 600 = 0 \\ \\ </p><p></p><p> \sf \to \: n^2 - 25n + 24n - 600 = 0 \\ \\ </p><p></p><p> \sf \to n(n - 25) + 24 (n + 25) = 0 \\ \\ </p><p></p><p> \sf \to \: (n - 25) (n + 24) = 0 \\ \\ </p><p></p><p> \sf \to \: n - 25 = 0 \: or \: n + 24 = 0 \\ \\ \sf \to \orange{ n = 25 \: or \: n = \: - 24}\: \huge \dag\\ </p><p></p><p>$

$\sf \underline{ \red{n = 25 } \: (Number \: of \: days \: cannot \: be \: negative)}$

$\text{ \green{ \underline{{Thus, the work is completed in 25 days.}}}}$