percentage question

[sandeepgupta176]

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)


Answer is D but no idea how to go about it....!!!

[amrita84]

I hope this helps - I found it hard too

number of News A sold = #a
number of news B sold = #b


r/100= $1 * #a /($1 * #a + $1.25 * #b)

p/100 = #a / (#a + #b)

r/(1-r) = ($1 * #a /($1 * #a + $1.25 * #b))/ (1 - ($1 * #a /($1 * #a + $1.25 * #b)))
= (#a/#a + 1.25#b)/ (((#a+1.25#b) - #a)/ (#a+1.25#b))

= (#a/#a + 1.25#b)/(1.25#b/ (#a + 1.25#b))
= #a/1.25#b

p/(1-p) = ((#a/(#a+#b))/((#a+#b - #a)/(#a + #b))
= #a/#b
#a = #b {(p/(1-p)}

r/ (1-r) = #b {(p/(1-p)} / 1.25 #b

r/ (1-r) = (p/((1-p)*1.25)

1.25 (1-p)/p = (1-r)/r
(1.25 - 1.25p)/p = (1/r) - 1
(1.25-1.25p+p)p = 1/r
r = p/ (1.25-0.25p)
r = (1/0.25)p/ (500-p)
r = 400p/(500-p)

[sandeepgupta176]

Thanks Amrita but I have found a better solution to the said problem...hope that helps you....

One Way
Assume 1 copy of newspaper A was sold and 0 copies of newspaper B was sold
P = Percentage of Copies A sold = 100
R = Percentage of Revenue from A = 100
By substituting the value of P we easily know that D is the only answer choice to equal 100.

Hence D.



Conventional Way
Let total number of papers be 100.
Hence, no. of newspaper A sold = p% of 100 = p
and no. of newspaper B sold = 100 - p.

Now r% of total revenue from papers comes from selling A.
Here total revenue from papers = p * 1 + (100 - p) * 1.25 = 125 - 0.25p
[revenue from A = p * 1 and from B = (100 - p) * 1.25]

Now %age of total revenue coming from A = revenue from A /total revenue * 100
= p/(125 - 0.25p) * 100
But it's already given that p/ (125-0.25p) *100 = r
Since all the answer options have p in the denominator, we'll have to remove 0.25 from the denominator. Simple observation leads us that multiplying by 400 will remove 0.25.
Hence, r = 400p/(500 - p). Ans (d)

[Ben Ku]

Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.