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### Ratio

by deepakb » Wed Oct 06, 2010 11:28 pm
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for$1.25 each, and the store sold no other newspapers that day. If r
percent of the store's revenues from newspaper sales was from Newspaper A and if p
percent of the newspapers that the store sold were copies of newspaper A, which of the
following expresses r in terms of p?

A. 100p / (125 - p)
B. 150p / (250 - p)
C. 300p / (375 - p)
D. 400p / (500 - p)
E. 500p / (625 - p)

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by shovan85 » Thu Oct 07, 2010 2:02 am
Total Revenue = 1*p + 1.25*(100 - p) = p + 125 -1.25p = 125 - 0.25p

So the total revenue of A = p/(125-0.25p)

This is equal to r% of total revenue.

So, r/100 = p/(125-0.25p)
=> r = 100p/(125 - p/4) = 400p / (500 - p)

IMO

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by GMATGuruNY » Thu Oct 07, 2010 3:30 am
deepakb wrote:Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for$1.25 each, and the store sold no other newspapers that day. If r
percent of the store's revenues from newspaper sales was from Newspaper A and if p
percent of the newspapers that the store sold were copies of newspaper A, which of the
following expresses r in terms of p?

A. 100p / (125 - p)
B. 150p / (250 - p)
C. 300p / (375 - p)
D. 400p / (500 - p)
E. 500p / (625 - p)
Let's plug in:
1 copy of A sold = $1 4 copies of B sold = 4*1.25 =$5
Total sold = 1+4 = 5.
p = 1/5*100 = 20
Total revenue = 1+5 = 6.
r = 1/6*100 = 50/3. This is our target answer.

Now we plug p=20 into all the answers to see which gives us our target of 50/3.

(400*20)/(500-20) = 8000/480 = 50/3.