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In a hostel, the number of students decreased by 8% and the

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In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?

A. 19%
B. 15%
C. 25%
D. 40%
E. 9.4%
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Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)

Originally,
C = FNP

When number of students decrease by 8%, and the price of food increases by 20%,
C = F(new) * (0.92N) * (1.2P)
=> F(new) = F/(0.92*1.2)
=> F(new) = 0.906F

Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4% (option E)
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Last edited by GyanOne on 26 Jun 2015, 23:21, edited 1 time in total.
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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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New post 20 Aug 2014, 09:58
I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.
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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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New post 20 Aug 2014, 23:08
speedilly wrote:
I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.


Agree.. this calculation goes tough. Any simpler way to avoid that 92 & 12 factor?
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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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PareshGmat wrote:
speedilly wrote:
I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.


Agree.. this calculation goes tough. Any simpler way to avoid that 92 & 12 factor?


Hello

My approach is

Name:
S = number of students
P = Price
Q = Quantity of food consumption.
C = total cost

==> C = S*P*Q

One way to solve this kind of question is plug in numbers.
Assume: before we have 100 students, P = $10 ==> C = 100*10*Q = 1000*Q
After: we have 92 students, P = $12 ==> C' = 92*12*Q' = 1104*Q'

==> 1104*Q' = 1000*Q
==> Q' = 1000/1104*Q = (1 - 104/1104)*Q
==> Q' = Q - 104/1104*Q

The red part is the decrease of food consumption. We can guess 104/1104 ~ 9.4% (The ONLY option < 10%) --> E is answer.

Hope it helps.
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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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New post 24 Jan 2015, 05:52
C - Comes out to be 9.42 %
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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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New post 14 Apr 2016, 02:09
Vyshak
Any Shortcuts here ?
took me 8 minutes to solve
i solved twice
actually thrice :)

regards
Stone Cold
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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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stonecold wrote:
Vyshak
Any Shortcuts here ?
took me 8 minutes to solve
i solved twice
actually thrice :)

regards
Stone Cold


Yes bro possible

IMHO that we need to take three factors ( No of Students , Consumption per student and Cost of Food ) and create a table as below -
Attachment:
1.PNG
1.PNG [ 4.07 KiB | Viewed 715 times ]


Where Total Cost = No of Students * Consumption per student * Cost of Food

So, from the above table find the new value of Consumption per student

Consumption per student = Total Cost / ( No of Students * Cost of Food )
=>Consumption per student = 10000 / 92 * 12
=>New Consumption per student = 9.06

Now find the last part -

Quote:
By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?


Reduction in consumption required is 10 - 9.06 = 0.94

So, Percentage consumption of food be cut short by every student = 0.94/10 * 100 = 9.40% :-D :lol:
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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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stonecold wrote:
Vyshak
Any Shortcuts here ?
took me 8 minutes to solve
i solved twice
actually thrice :)

regards
Stone Cold


Hi,

Assume there are 100 students, price/student = 10, Consumption = 1unit --> Cost = 100*10*1 = 1000
Given scenario: 92 students, price/student = 12, Consumption = x, But cost = 1000

92*12*x = 1000
x = 1000/1104 = 125/138 = 0.9 (approx)
So consumption has reduced by (1 - 0.9)*100 = 10% (approx)

Answer: E
Re: In a hostel, the number of students decreased by 8% and the   [#permalink] 14 Apr 2016, 03:07
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