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# A certain retailer decided to raise its prices by p%. When, as a resul

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Re: A certain retailer decided to raise its prices by p%. When, as a resul [#permalink]
Bunuel wrote:
A certain retailer decided to raise its prices by p%. When, as a result, its sales dropped by q%, the retailer found that its total revenue was unchanged. Which of the following correctly expresses q in terms of p?

A. p
B. 1/p
C. p/(1−p)
D. 100/(100+p)
E. 100p/(100+p)

Let, 100 is increased by 25% (p%) so it becomes 125

Now we need to decrease it by 20% (q%) to bring it to the same level i.e. 100

So, p=25 and q=20 satisfies the requirement. Verify the options

A. p This is not equal to q hence INCORRECT
B. 1/p = 1/25 This is not equal to q hence INCORRECT
C. p/(1−p)= 25/(1-25) This is not equal to q hence INCORRECT
D. 100/(100+p) = 100/(100+25) This is not equal to q hence INCORRECT
E. 100p/(100+p) = 100*25/(100+25) = 20 This is equal to q hence CORRECT

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Re: A certain retailer decided to raise its prices by p%. When, as a resul [#permalink]
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Bunuel wrote:
A certain retailer decided to raise its prices by p%. When, as a result, its sales dropped by q%, the retailer found that its total revenue was unchanged. Which of the following correctly expresses q in terms of p?

A. p
B. 1/p
C. p/(1−p)
D. 100/(100+p)
E. 100p/(100+p)

We can let n = number of items and x = price per item.

Since the price was raised by p%, the sales dropped by q%, and revenue remained the same, we have:

nx = [1+(p/100)]x * [(1-(q/100)]n

1 = [(100+p)/100][(100-q)/100]

1 = (100+p)(100-q)/10,000

10,000 = 10,000 + 100p - 100q - pq

100q + pq = 100p

q(100 + p) = 100p

q = 100p/(100 + p)