pikachu wrote:

udaymathapati 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)

This problem can be easily solved by picking numbers. The explanation given in the

OG can be very laborious.

Lets say the number of newspaper A sold = 20, so revenue from A = 20 and the number of newspaper sold from B = 80, so revenue from B = 100. Now total revenue =120 out of which 20 came from A. So

r (A) = 20/120 = 1/6 = 16.7% and p (A) = 20/100 *100 = 20

A) 100*20/(125-20) -> Incorrect

B) 150*20/(250-20) -> Incorrect

C) 300*20/(375-20) -> Incorrect

D) 400*20/(500-20) = 8/48 = 1/6*100 = 16.7% - > Correct

E) 500*20/(625-20) -> Incorrect

So Ans D

This problem was definitely something to work on. I was able to understand it with Pikachu’s help, although, the calculations were not very clear (substitution of P in % and in Number).

So, I am going to try and put it in my own vision of explanation, using number pickings as suggested, since algebraic calculations is really long and seems very confusing to me. Please correct my mistakes.

So what we have here is:

Newspapers A sold – $1/piece

Newspaper B sold – $1.25/piece

r - % of revenue generated from A newspapers sales

p - % of A newspapers sold.

Let’s use a and b as numbers of A & B np sold.

a + b = a total number of newspapers sold.

% of something = (part/whole)*100%. => p = (a/(a+b))*100%

now r % = (Revenue of A/Revenue A + Revenue B)*100% =>

R(total) = RevenueA +RevenueB. (revenue = price * number of pieces sold)

Having price np A sold and 1$/piece and np B sold 1.25$/piece the formula is as follows:

R(total) =1$*a + 1.25$b or = a + 1.25b

r = (a/(a+1.25b))*100%

Now let’s use numbers:

20 np A sold

80 np B sold.

Total np sold = 100.

p (% of np A sold) = 20%

Total revenue R = (1$*20 + 1.25$*80) = 20 + 100 = 120$

r (% of revenue A sold) = (20$/120$)*100% = 16.7%

Now lest try and plug in the numbers. We are looking for r = 16.7%, the final result is to be multiplied to 100%. Also in numerator we will be p in % as 0.2, and denominator – we are using p – as a number – 20 (number of A newspapers sold in pieces and not in %)

(a) (100(pieces)*0.2)/(125(pieces) – 20(pieces)) = (20/105)*100 = 19% - incorrect

(b) (150*0.2)/(250 – 20) = 30/230 = 3/23 = 13% => incorrect

(c) (300*0.2)/(375 – 20) = 12/71 = 16,9 % (we are looking for 16,7%) => incorrect

(d) (400*0.2)/(500-20) = 1/6 = 16.7% - correct.

(e) (500*0.2)/(635 – 20) = 100/615 = 50/123 = 40%. => incorrect

Now let’s check it and pick other numbers:

40 np A sold

60 np B sold

Total np sold are 100. R total = 115$

p = 40%, 40 in $

r = 34.7% or ~ 35%.

(a) 100*0.4/(125 – 40) = 8/17= 47% => incorrect

(b) 150*0.4/(250 – 40) = 6/21 = 29% => incorrect

(c) 300*0.4/(375 – 40) = 24/17 ~ 36% (again close but incorrect)

(d) 400*0.4/(500 – 40) = 8/23 = 34.7% correct

(e) 500*0.4/(625 – 40) = 40/117 = 34%

Seems like D is a correct answer for both. Please correct me if I am making any errors in understanding the concept of how to approach this problem, since, the way I see it – it is a key to solving it in 2 minutes.