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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 [#permalink] New post 01 May 2012, 20:22
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Question Stats:

63% (03:13) correct 37% (02:43) wrong based on 79 sessions
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%
[Reveal] Spoiler: OA
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Re: hostel students food consumption - Percents problem [#permalink] New post 01 May 2012, 22:23
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Cost of food (C) = Food consumer 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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Intern
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Re: In a hostel, the number of students decreased by 8% and the [#permalink] 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] 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] New post 21 Aug 2014, 00:04
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] 21 Aug 2014, 00:04
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