Problem Solving

A school's annual budget for the purchase of student computers increased by 60% this year over last year. if the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?

a. 33 1/3%
b. 40%
c. 42%
d. 48%
e. 60%

Answer is A

Let's assume that the school's annual budget was x dollars last year. It'd be 1.6x dollars this year since its annual budget increased by 60% from last year this year. In addition to that, let's say that the school bought computers for y dollars each last year, and bought a total of x/y computers. Since the price of computers increased by 20% from last year to this year, the school bought 1.6x/1.2y or 4x/3y computers this year. Because the question is asking for the percent increase in the school's purchase of computers from last year to this year, we can say that the correct answer is 33.33% since 4x/3y= 1.3333x/y.

Lets pick easy numbers for budget and price of each computer

100 160
100 120

No of computers last year = 1
No of computer this year = 4/3

%inc = New-Old/old * 100
= 4/3-1/1*100
= 33 1/3%

Let N be the number of computers purchased last year

Since the fund is increase by 60%, if there is no change in the price, the number of computer purchased this year will be 160%(N).

But since the price of the computer is increased by 20% i.e. the price has become 6/5, the number of computers that can be purchased will be 5/6 x 160%(N) = 133.335(N).

Hence the increase is 33.33%