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A team of workers was employed by a contractor who undertook to finish

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Bunuel
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A team of workers was employed by a contractor who undertook to finish [#permalink] New post   21 Jan 2021, 10:00
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A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. If the team were to make four more pieces per day than was planned, they would complete the job a day ahead of the schedule. How many days did the team take to complete the job at the original rate?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 13
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C
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Re: A team of workers was employed by a contractor who undertook to finish [#permalink] New post   21 Jan 2021, 18:25
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Let the number of days taken = x

Number of articles made per day = \(\frac{360}{x}\)

When number of articles per day is increased by 4, then the number of days reduced by 1.

i.e \(\frac{360}{x - 1} = \frac{360}{x} + 4\)

Therefore 360x = 360(x - 1) + 4(x)(x-1)

\(360x = 360x - 360 + 4x^2 - 4x\)

\(4x^2 - 4x - 360 = 0\)

\(x^2 - x - 90 = 0\)

\(x^2 - 10 + 9x - 90 = 0\)

x(x - 10) + 9(x - 10) = 0

x = -9 or x = 10


Option C

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Re: A team of workers was employed by a contractor who undertook to finish [#permalink] New post   22 Jan 2021, 01:04
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Let x be the no of days and p be the no of units produced each day
xp = 360
and (x-1)(p+4)=360
x = 10
In how many days did they COMPLETE = x-1 = 9
B
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Re: A team of workers was employed by a contractor who undertook to finish [#permalink] New post   24 Jan 2021, 23:39
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Bunuel wrote:
A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day than was planned, they could complete the job a day ahead of schedule. How many days did they take?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 13


Hi Bunuel, I feel the question is asking " how many days the work was completed after the rate of output was increased ". Hence, I went with B. Could you please point out the flaw in my approach?
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Re: A team of workers was employed by a contractor who undertook to finish [#permalink] New post   24 Jan 2021, 23:48
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ShankSouljaBoi wrote:
Bunuel wrote:
A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day than was planned, they could complete the job a day ahead of schedule. How many days did they take?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 13


Hi Bunuel, I feel the question is asking " how many days the work was completed after the rate of output was increased ". Hence, I went with B. Could you please point out the flaw in my approach?


Agree, the wording could have been better. Edited the question. Hope now it's better.
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Re: A team of workers was employed by a contractor who undertook to finish [#permalink] New post   10 Apr 2021, 17:37
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This seems like an easy one to do trial and error with the answers:

A) 360/8 = 45 units per day
B) 360/9 = 40 units per day
C) 360/10 = 36 units per day
D) 360/12 = 30 units per day
E) 360/13 = 27ish or 28ish units per day

Notice the difference between B & C is 4 units per day, hence B must be the +4 unit rate and C must be the original rate, hence C is the answer. Good strategy for plugging answers is to start with C, so if you were lucky enough to start with C and go up this took very little math.
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Re: A team of workers was employed by a contractor who undertook to finish [#permalink] New post   25 Dec 2023, 07:48
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Re: A team of workers was employed by a contractor who undertook to finish [#permalink]
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