Girish bought a car and got a dealer’s discount of 15% on the original

Thanks for the solution, just 1 question though
while calculating the profit percentage why are you using 100 instead of 85 in 1st case and instead of 88 in the 2nd case.
Thanks in advance

The exact words in the question regarding the quantity that we need to calculate is "What would be the difference in the profit percentages of the two transactions?". Now, there are two possible ways to interpret "profit" in this question: the actual profit that the dealer makes (i.e. the dealer's selling price - the amount the dealer paid for the price), and profit over the original price (i.e. the dealer's selling price - the original price of the car without discount). This question actually makes sense only if we use the latter interpretation. Expressed as a percent, the former is actually 20% for both scenarios. Let's verify this:

If we calculate the profit percentage when the dealer pays $85 and sells for $102, we get (102 - 85)/85 = 17/85 = 20%.

If we calculate the profit percentage when the dealer pays $88 and sells for $105.6, we get (105.6 - 88)/88 = 17.6/88 = 20%.

As you can see, using the numbers you mentioned, one calculates the difference between the profit percentages as 20 - 20 = 0, which is not even among the answer choices. That is why we should use the profit based on the original price in this question.

can someone explain why -3 and -2.4 in the above solution?

Couldnt the word same mean 12 %?

The best method to solve this problem is by successive percentage calculation method:
Case 1: -15 + 20 - (-15*20/100) = 2
Case 2: -12 + 20 + (-12*20/100)= 5.6
Therefore difference 5.6-2= 3.6

Posted from my mobile device

Hi SaurabhPatil20 could you explain your reasoning behind the numbers?

Edit: I see that this is the concept used https://gmatclub.com/forum/excellent-method-for-calculating-successive-percentages-185973.html#p1423049

Thanks

CASE - I

Let Original Price be 100 ; Discounted Price will be 85 , SP will be 112% of 85 = 95.20


CASE - II

Let Original Price be 100 ; Discounted Price will be 88 , SP will be 112% of 88 = 98.56

Difference in the profit percentages of the two transactions will be (98.56-95.20)/95.20*100 ~ 3.60%, Answer must be (B)

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