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

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Joined: 04 Mar 2012
Posts: 46
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Kudos [?]: 17 [0], given: 10

In a hostel, the number of students decreased by 8% and the [#permalink]  01 May 2012, 20:22
00:00

Difficulty:

45% (medium)

Question Stats:

66% (03:28) correct 34% (02:42) wrong based on 58 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
Director
Status:
Joined: 24 Jul 2011
Posts: 547
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 60

Kudos [?]: 261 [1] , given: 11

Re: hostel students food consumption - Percents problem [#permalink]  01 May 2012, 22:23
1
KUDOS
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)

_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

Re: hostel students food consumption - Percents problem   [#permalink] 01 May 2012, 22:23
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