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.

Please help me ​

Answer 1

Answer:

Let x be the number of days in which 150 workers finish the work.

According to the given information 150 × = 150 + 146 + 142....(x+8) teams.

The series 150 + 146 + 142 + .... (x+8) teams in an A.P . With first team 146 . Common difference a€"4 and number of teams as (x+8)

$➻ \: 150 = \frac{(x + 8)}{2} [2(150) + (x + 8 - 1)( - 4)]$

$➻ \: 150 = (x + 8)[150 + (x + 7)( - 2)]$

$➻ \: 150x = (x + 8)(150 - 2x - 14)$

$➻ \: 150 = (x + 8)(136 - 2x)$

$➻ \: 75x = (x + 8)(68 - x)$

$➻75x = 68 - {x}^{2} + 544 - 8x$

$➻{x}^{2} + 75x - 60x - 544 = 0$

$➻ \: {x}^{2} + 15x - 544 = 0$

$➻ \: {x}^{2} + 32x - 17x - 544 = 0$

$➻ \: x(x + 32) - 17(x + 32) = 0$

$➻ \: (x - 17)(x + 32) = 0$

$➻ \: x = 17 \: or \: x = - 32$

However,x cannot be nagative

➫ x = 17

Therefore, originally, the number of days in which completed is 17.

Thus, required number of days

➫ (17 + 8 ) 25

Answer 2

Let x be the number of days in which 150 workers finish the work.

According to the given information 150 × = 150 + 146 + 142....(x+8) teams.

The series 150 + 146 + 142 + .... (x+8) teams in an A.P . With first team 146 . Common difference a€"4 and number of teams as (x+8)

➻150=2(x+8)[2(150)+(x+8−1)(−4)]

➻150=(x+8)[150+(x+7)(−2)]

➻150x=(x+8)(150−2x−14)

➻150=(x+8)(136−2x)

➻75x=(x+8)(68−x)

➻75x=68−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=17orx=−32

However,x cannot be nagative

➫ x = 17

Therefore, originally, the number of days in which completed is 17.

Thus, required number of days

➫ (17 + 8 ) 25