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

Answer: Option E

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