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

Question

Girish bought a car and got a dealer’s discount of 15% on the original price. He sold it at a profit of 20% on the purchase price. If he had got a discount of 12% on the original price and had sold it for the same profit percentage of the purchase price, what would be the difference in the profit percentages of the two transactions?

A 2%
B 3.6%
C 5%
D 5.6%
E 8%

A 2%
B 3.6%
C 5%
D 5.6%
E 8%

Dashingnightmare · Answer

B.
case 1: 20-15-3 =2%
case 2: 20-12-2.4=5.6%
Difference =5.6-2= 3.6% Hence B.

ScottTargetTestPrep · Answer

Solution:
 
Let’s assume that the original price of the car was $100. Thus, for the first transaction, Girish paid 100 x 0.85 = $85 for the car. He sold the car for 85 x 1.2 = $102, which is a profit of $2 over the original price of the car of $100. Thus, his profit (based on the original price) is 2/100 = 2%.

For the hypothetical second transaction, he would have paid 100 x 0.88 = $88 for the car. He would have sold the car for 88 x 1.2 = $105.6, which is a profit of $5.60 over the original price of the car. Thus, his profit would have been 5.6/100 = 5.6%.

The difference in the profit percentages is 5.6% - 2% = 3.6%.

Answer: B

ShaikhMoice · Answer

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

ScottTargetTestPrep · Answer

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.

harvar · Answer

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

GreatII · Answer

Couldnt the word same mean 12 %?

SaurabhPatil20 · Answer

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

StringArgs · Answer

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

Abhishek009 · Answer

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

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