Newspapers A & B

[kayser]

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)

[sureshbala]

Folks, the quicker way to answer this is......

Since for any given value of p and r the answer must be same.....

Take p =100 i.e the shop sold only newspaper A.

Then obviously r also will be100.

So r = p.

Now substituing p =100 in the options , the options that gives r = p are B & D.

Now if p =50, since equal number of papers are sold, the revenue will be in the ratio of 1: 1.25 = 4:5. Hence r = 4/9(total sales)

Only D satisfies this...

[sureshbala]

Folks, even if you want to do it normally, it should not take much time...

Let S be the total sales and M be the total money realized.

For convenient calculations take price of A as 100$ and B as 125$.

Given that number of papers A sold is p%(S)

So revenue from the sales of A will be p%(S)(100). [Obviously revenue from the sales of B will (100-p)%(S)(125)]

It is given that p%(S)100 = r%(M)

So r = 100p(S/M)

Also total revenue M = p%(S)100 + (100-p)%(S)125
M = S%(100p+12500-125p) = S%(12500-25p)

Substituting this value of M in r = 100p(S/M), we get

r = 100p(100/12500-25p)

Since in all the options, the denominator is just p, divide the Nr and Dr with 25 and hence we get

r = 400p/(500-p)

[sureshbala]

Folks, even if you want to do it normally, it should not take much time...

Let S be the total sales and M be the total money realized.

For convenient calculations take price of A as 100$ and B as 125$.

Given that number of papers A sold is p%(S)

So revenue from the sales of A will be p%(S)(100). [Obviously revenue from the sales of B will (100-p)%(S)(125)]

It is given that p%(S)100 = r%(M)

So r = 100p(S/M)

Also total revenue M = p%(S)100 + (100-p)%(S)125
M = S%(100p+12500-125p) = S%(12500-25p)

Substituting this value of M in r = 100p(S/M), we get

r = 100p(100/12500-25p)

Since in all the options, the denominator is just p, divide the Nr and Dr with 25 and hence we get

r = 400p/(500-p)

Folks, in the above calculation you can make a slight variation and make it very quick.....

Revenue from A i.e p%(S)(100) = r%(M)---------(a)

Revenue from B i.e (100-p)%(S)(125) = (100-r)%(M)-----(b)

(a)/(b) = 4p/(500-5p) = r/(100-r)

i.e 400p - 4pr = 500r - 5pr

i.e 400p = 500r - pr

Hence r = 400p(500-p)

Definitely this is quicker than previous calculation