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.​

Answer 1

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

• A.T.Q ☞

150x=150+146+142+...(x+8)terms

150+146+142+...+(x+8) terms is an A.P.

• •first term 150,

• •common difference -4

• number of terms as (x+8).

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⇒150x= x+8/2 [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

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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 2

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

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 negative

➫ x = 17

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

Thus, required number of days

➫ (17 + 8 ) = 25

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