Percentage

[dhairya275]

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%
15%
[C] 25%
[D] 40%
[E] 9.4%

[truplayer256]

Assume the original number of students was s and the price of food per pound was f. Then for the year after that:
# of students= 0.92s
Price per lb of food = 1.20f
Total cost of food for first year = sf
Total cost of food for second year = (1.20)(0.92)(sf)= 1.104sf
This value must be multiplied by 0.906 to get sf so there should be a decrease of 9.4% decrease in food consumption.

[GMATGuruNY]

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%
15%
[C] 25%
[D] 40%
[E] 9.4%

Let the number of students = 100 and the original cost per student = 10.
Total cost = 100*10 = 1000.

The number of students decreased by 8% = 92.
The cost per student increased by 20% = 12.
New total cost = 92*12 = 1104.

For the amount spent this year to be the same as the amount spent the previous year, the new total cost must be reduced from 1104 to 1000 -- a decrease of about 10%.
Thus, each student must consume about 10% less food.

The correct answer is E.