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If 45 people built 1/2 of a pyramid in 288 days, how many days did it

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Bunuel
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If 45 people built 1/2 of a pyramid in 288 days, how many days did it [#permalink] New post   09 Oct 2018, 01:11
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If 45 people built \(\frac{1}{2}\) of a pyramid in 288 days, how many days did it take 65 people to build the next \(\frac{1}{6}\) the pyramid, rounded to the nearest integer, assuming each person works at the same constant rate?


(A) 66 days

(B) 77 days

(C) 88 days

(D) 87 days

(E) 76 days
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apurva908
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Re: If 45 people built 1/2 of a pyramid in 288 days, how many days did it [#permalink] New post   09 Oct 2018, 04:38
45 people complete the job in 288x2 days
total man days= 288x2x45
65 man will complete the job in 288x2x45/65 days
65 man will comlete 1/6th of the job in 288x2x45/(65x6)= 66 days
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Re: If 45 people built 1/2 of a pyramid in 288 days, how many days did it [#permalink] New post   09 Oct 2018, 08:30
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Bunuel wrote:
If 45 people built \(\frac{1}{2}\) of a pyramid in 288 days, how many days did it take 65 people to build the next \(\frac{1}{6}\) the pyramid, rounded to the nearest integer, assuming each person works at the same constant rate?

(A) 66 days

(B) 77 days

(C) 88 days

(D) 87 days

(E) 76 days


\(\frac{M_1 D_1}{W_1} = \frac{M_2 D_2}{W_2}\)

Or, \(\frac{45*288}{1/2} = \frac{65* D_2}{1/6}\)

Or, \(45*288*2 = 65*2*D_2\)

So, \(D_2 ~ 66\), Answer must be (A) 66
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Re: If 45 people built 1/2 of a pyramid in 288 days, how many days did it [#permalink] New post   12 Oct 2018, 07:55
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Bunuel wrote:
If 45 people built \(\frac{1}{2}\) of a pyramid in 288 days, how many days did it take 65 people to build the next \(\frac{1}{6}\) the pyramid, rounded to the nearest integer, assuming each person works at the same constant rate?


(A) 66 days

(B) 77 days

(C) 88 days

(D) 87 days

(E) 76 days


The rate of 45 people is (1/2)/288 = 1/576, which means that 45 people can build 1/576 of a pyramid in one day.

We can use a proportion to determine the rate x of 65 people:

45/(1/576) = 65/x

45 * 576 * x = 65

9 * 576 * x = 13

x = 13/5184. This value 13/5184 means that 65 people can build 13/5184 of a pyramid in one day.

So, to build 1/6 of a pyramid, it will take 65 people (1/6)/(13/5184) = 5184/78 ≈ 66 days.

Answer: A
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Re: If 45 people built 1/2 of a pyramid in 288 days, how many days did it [#permalink]
12 Oct 2018, 07:55
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