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

Question

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%

Show Answer

Official Answer

E

A. 19% 
B. 15% 
C. 25%
D. 40% 
E. 9.4%

Abhishek009 · Accepted Answer

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 - 1.PNG 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 - 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

GyanOne · Answer

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)

GSBae · Answer

I cannot see this being a GMAT problem - how is one supposed to calculate 1-   without a calculator? Even with using fractions I get 13/138 which is also not easily solved.

PareshGmat · Answer

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

pqhai · Answer

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.

stonecold · Answer

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

regards Stone Cold

Kurtosis · Answer

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

hellosanthosh2k2 · Answer

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)

exc4libur · Answer

just to clear things up, what you did in the second part was:
C = F(new) * (0.92N) * (1.2P)
FNP = F(new) * (0.92N) * (1.2P)
F(new) = FNP / (0.92N) * (1.2P)
F(new) = F / (0.92) * (1.2)
F(new) = 0.906F

correct?

Harsht7 · Answer

Rule: If the overall/final value is not changing and if one variable is increased by $\frac{1}{x}$% then the other variable should decrease by $\frac{1}{x+1}$%
for eg: if AB = 100, now if B is increased by $33.33$% then by how much percentage should A decrease such that the final value remains the same.
Now, B is increased by $33.33$% --> $\frac{1}{3}$% --> $x=3$
Then if final value is same, i.e; 100, then A should decrease by $\frac{1}{x+1}$% = $\frac{1}{(3+1)}$% = $\frac{1}{4}$% = $25$%

To be more clear - let $A = 20$ and$ B = 5$ --> $AB = 20*5$ = $100$
Now if $B = 5$ is increased by $33.33$% = $5*1.3333$ = $6.6665$, then $A = 20$ should decrease by $25$% = $20*0.75$ = $15$,
such that $AB = 6.6665*15$ = $99.997$ =$~100$ (same as before)

We can apply the same logic here
Let say, Total consumption = $T$
consumption of food / student = $c$
total number of students = $n$
price per food = $p$

Hence,
$T = c * n * p$

Let us take $n * p = F$

So, $T = c * F$

Now, $n$ is decreased by $8$% and $p$ is increased by $20$%, we can calculate overall % change in $F$ by formula $A + B + \frac{AB}{100}$
overall % change in $F$ = $20 - 8 - \frac{20(8)}{100}$ = $10.4$%

Total consumption(after change), $T = c' * 10.4F$, where $c'$ = change in the consumption

Now, let's apply the above logic we learned,

The total consumption $T$ is same and one variable $F$(here) is increased by $10.4$% ~ $10$%(approximate) = $\frac{1}{10}$% = $x = 10$

Hence the other variable $c'$ (here) should decrease by $\frac{1}{x+1}$% = $\frac{1}{(10+1)}$% = $\frac{1}{11}$% = $9.09$% ~ $9$%

The only answer option closest to $9$% = $9.4$% Option E

Kudos if find solution helpful

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