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In a hostel, the number of students decreased by 8% and the
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01 May 2012, 20:22
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69% (02:46) correct 31% (02:50) wrong based on 223 sessions
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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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In a hostel, the number of students decreased by 8% and the
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Updated on: 26 Jun 2015, 23:21
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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Originally posted by GyanOne on 01 May 2012, 22:23.
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
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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
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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
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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*QThe 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
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14 Apr 2016, 02:09



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Re: In a hostel, the number of students decreased by 8% and the
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14 Apr 2016, 02:51
stonecold wrote: VyshakAny 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 [ 4.07 KiB  Viewed 2512 times ]
Where Total Cost = No of Students * Consumption per student * Cost of FoodSo, 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%
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Re: In a hostel, the number of students decreased by 8% and the
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14 Apr 2016, 03:07
stonecold wrote: VyshakAny 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



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Re: In a hostel, the number of students decreased by 8% and the
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09 Feb 2018, 09:58
Let there be 100 students , price of each food student be 100$ Now 8% number of students reduced = 92, price of food increased by 20% = 120$ x(x is decimal less than 1) be reduced consumption of food, so price of reduced food = 120x
given 100 * 100 = 92 * 120 * x x = 10000/(92*120) = 1000/1104 = 10/11 (approx) so how much each student has to reduce = 1  10/11 = 1/11 = 9% approx => closest is (E)




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