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

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

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05 Jul 2017, 00:41
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Question Stats:

49% (02:06) correct 51% (02:57) wrong based on 141 sessions

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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.

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

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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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05 Jul 2017, 14:31
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1
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.

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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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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

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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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11 Jul 2018, 23:45
@Bunnel chetan2u
can you provide the official explanation?
I think i am doing wrong here in formulating the equation

Let the total time taken to be taken by 100 soldiers be: T
Statement 1
let time after 13 days time taken by 200 soldiers to complete the remaining ration = a
13*100+ 200a = 100T+12*200
1300+200a = 100(a+13)+ 2400
200a=100a+2400
100a=2400
a=24
hence total time = 24+13 =37
sufficient
Statement B
100T = 80*1.25T
Hence insufficient
Kindly clarify
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For how many days are rations expected to last in a camp of 100 soldie [#permalink]

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12 Jul 2018, 00:22
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.
a) logically...
since they eat same amount of food, if 200 eat some quantity for 12 days, 100 will eat same quantity for 12*2=24
so the ration will last for 13+24=37 days
b) algebraic method
total days if counted for 100 initially and then 200 = $$13*100+200*12=1300+2400=3700$$
total days when counted on 100 soldiers taking them as x days = 100x
$$100x=3700.........x=37$$
Raksat algebraic should be on these lines.
sufficient

(2) If 20 soldiers leave the camp in the very beginning, the rations would last for 25 percent more number of days.
let x be the days initialy so 100x but with 20 moving out remaining use it for 1.25x
so 100x=1.25x*80......100x=100x
it will always be true....
reduction in 20 out of 100 or 20% would always increase days by 25%
insuff

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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12 Jul 2018, 01:01
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 consumption rate per soldier be 1 unit of ration per day.

Hence 100 soldiers will consume 100 units of ration per day.

Let n be the # of days the ration can last for 100 soldiers. Hence Total ration for 100 soldiers is 100n

Statement 1: For 13 days ration consumed by 100 soldiers is 13*100 = 1300 units

Remaining ration = 100n - 1300

100 additional soldiers, along with 100 original consume the remaining ration in 12 days.

Hence 200*12 = 100n -1300

n = 27

Statement 1 is Sufficient.

Statement 2: 20 soldiers leave the camp at the beginning. Hence only 80 soldiers left to consumer 100n units of ration.

80 soldiers consume 80 units per day, therefore # of days the ration lasts for them = 100n/80 =5n/4 days

the # of days given is 25% more, which is 1.25n = 5n/4 days

we get same information, No additional information provided.

Statement 2 is Not Sufficient.

Thanks,
GyM
Re: For how many days are rations expected to last in a camp of 100 soldie   [#permalink] 12 Jul 2018, 01:01
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# For how many days are rations expected to last in a camp of 100 soldie

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