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For how many days are rations expected to last in a camp of 100 soldie

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For how many days are rations expected to last in a camp of 100 soldie [#permalink]

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New post 05 Jul 2017, 00:41
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For how many days are rations expected to last in a camp of 100 soldiers? Assume that each soldier consumes equal quantities of rations per day.

(1) If 100 additional soldiers join the camp after 13 days, each consuming the same quantity of ration as the initial soldiers, the rations would last another 12 days.
(2) If 20 soldiers leave the camp in the very beginning, the rations would last for 25 percent more number of days.
[Reveal] Spoiler: OA

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For how many days are rations expected to last in a camp of 100 soldie [#permalink]

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New post 05 Jul 2017, 02:11
Bunuel wrote:
For how many days are rations expected to last in a camp of 100 soldiers? Assume that each soldier consumes equal quantities of rations per day.

(1) If 100 additional soldiers join the camp after 13 days, each consuming the same quantity of ration as the initial soldiers, the rations would last another 12 days.
(2) If 20 soldiers leave the camp in the very beginning, the rations would last for 25 percent more number of days.


let the daily consumption of soldier be x
question will be for how many days will ration last (ration/100x)?

(1) gives us 100*13*x + 200*x*12 = ration
ration = 2700x
days will be 27

Sufficient

(2) ration/100x = y
ration/80x = z
z = 1.25 y
Saved ration is 20x = 1.25y
We dont know the value of x hence Not sufficient

Assume each soldier requires 1 kg and hence ration is 100 kg for y day (total ration is 2000kg)
Now 80 soldier will require 80 kg for 1 day and hence will survive 1.25 days
100y/80 = 1.25
We can solve to get the value of y

Sufficient
Hence D

I think second part can have a better approach. Bunuel Please help
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Re: For how many days are rations expected to last in a camp of 100 soldie [#permalink]

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New post 05 Jul 2017, 14:31
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Let quantity of Ration consumed by each soldier per day = R

Let the current quantity of ration last for 'N' days for 100 soldiers

Therefore, Total Ration = 100 * R * N

We need to find the value of N.

Statement 1:If 100 additional soldiers join the camp after 13 days, each consuming the same quantity of ration as the initial soldiers, the rations would last another 12 days.

Ration consumed by 100 soldiers in 13 days = 100 * R * 13 = 1300 * R
Total Ration remaining = (100 * R * N) - (1300 * R)
Remaining Rations would last for 12 days for 200 soldiers

Therefore, 200 * R * 12 = (100 * R * N) - (1300 * R)

==> 24 = N - 13

==> N = 37

This statement is sufficient.

Statement 2: If 20 soldiers leave the camp in the very beginning, the rations would last for 25 percent more number of days.

If 20 soldiers left, then 80 soldiers will remain.

Rations would last for 25 percent more number of days = 1.25 * N = 1.25N

Therefore, 80 * R * 1.25N = 100 * R * N

As we see we do not get the value of N from above, this statement is not sufficient.

Answer is A.
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Re: For how many days are rations expected to last in a camp of 100 soldie [#permalink]

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New post 31 Dec 2017, 08:16
Let \(t\) be total number of rations initially and \(r\) be daily consumption per soldier

Statement 1 : (1) If 100 additional soldiers join the camp after 13 days, each consuming the same quantity of ration as the initial soldiers, the rations would last another 12 days.

Rations consumed during first 13 days = \(13 * 100 * r\)
so \((t - 1300r)/113r = 12\)
rearranging, \(t = 2656r\)

days rations can last = \(2656 r / 100 r\) (daily consumption by all soldiers) = 27 days

Sufficient

Statement 2: If 20 soldiers leave the camp in the very beginning, the rations would last for 25 percent more number of days.

Let t be number of days it can last.

as per this statement, \(100 * r * t = 80 * r * (5/4) t\) => \(100 * r * t = 100 * r * r\) => this statement does not say anything new => InSuff

Answer (A)
Re: For how many days are rations expected to last in a camp of 100 soldie   [#permalink] 31 Dec 2017, 08:16
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For how many days are rations expected to last in a camp of 100 soldie

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