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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]
these kind of problems can be solved easily by plug in some no. and whenever we see variables in questions the easy way to tackle them by plugging in no. for this we can take some easy no such as let's say revenue=sales(#of products)*price
now initial revenue was 300=30*10 and now after increasing price which is P by 50% we get price =45*q=300 and solving for q we get 20/3 and to calculate declining % we do 1-20/3=10/30*100 that 100/3 so q is =100/3% now we can substitute these values in options , that only option E provides 100/3 hence answer must be E
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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