Annie bought a mobile and sold it to Ben at a profit of 50%. After few

Question

Annie bought a mobile and sold it to Ben at a profit of 50%. After few days, Ben sold it back to Annie at 40% loss, and then Annie sold it to Charlie at 30% profit. Find the overall profit percentage of Annie?

A. 40.53%
B. 77%
C. 87%
D. 90%
E. 95%

A. 40.53%
B. 77%
C. 87%
D. 90%
E. 95%

IanStewart · Accepted Answer

There's no reason to do any work with these answer choices -- she makes a 50% profit on one of her sales, and a 30% profit on the other, so her overall profit percentage is somewhere between 30% and 50%, and answer A is the only logical possibility. If we did want an exact answer:

We can imagine the mobile costs $100. Then she first sells it to Ben for $150. At this point her total expenses are $100, and her total revenue is $150.

Then Ben sells the phone back to Annie for 40% less than $150, so for $90. So now her total expenses are $190.

Then she sells the phone for 30% more than $90, so for $117. Now her total revenue is $267.

So her profit percentage, which is her profit divided by expenses, is (267-190)/190 = 77/190. That's roughly 40%.

GMATWhizTeam · Answer

Solution:

Let the cost price of mobile for Annie be $100
 • Annie sold it at the profit of 50% to Ben
 o Profit =  \frac{50}{100}*100 =50 
• Now, cost price for Ben = $150
 o Ben sold it back to Annie at 40% loss
o Loss = \frac{ 40}{100}*150 = 60
o SP = 150- 60 = 90 
• Annie bought it back for 90
• Annie sold it for 30% profit to Charlie
 o Profit =  \frac{30}{100}*90 =27
o SP = 90+ 27 = 117 
• Effectively Annie earned = 150 - 90 + 117 = $177
 o Profit = 177 – 100 = $77
o Profit percentage =  \frac{77}{100} *100= 77%  
Hence, the correct answer is Option B.

mykrasovski · Answer

Hi  Bunuel , what is the source of the question? The answer should be (A). Annie spent $100 and $90 on a mobile, and sold it for $150 and $117.

Annie's revenue is $150+$117=$267.
Annie's cost is $100+$90=$190.

Profit $ = revenue - cost. Profit % = 100% * (revenue-cost)/cost, i.e. 100% * ($267-$190)/$190 = 40%.

Answer (A).

P.S. I would be darned to learn that people of such caliber as  IanStewart  make mistakes on such questions.

IanStewart · Answer

Thanks, but I do make mistakes sometimes! The problem here though is that the question is ambiguous. I just noticed that the OA was published, and is given as B, but that's only the right answer if you interpret the meaning of the question in a particular way (a way that seems unnatural to me). If you make a batch of sales, and you want to find your profit percentage, you just divide your total profit on the sales by your total expenses. That's how I've interpreted the meaning of this question, and then the answer is roughly 40%. If the answer to this question is meant to be 77%, then a different interpretation is intended. Instead, the question means to ask "Annie invested $x in a phone. Then she made this sequence of sales and purchases. What was her profit on her initial $x investment?" Under that interpretation, the answer is indeed 77%, but that's not how I interpret the phrase "profit percentage". Anyway, the question needs to be worded more carefully so its correct interpretation will be clear to anyone answering it.

ScottTargetTestPrep · Answer

We can let the mobile = $100 when Annie first bought it. So she sold it to Ben for 100 x 1.5 = $150, and Ben sold it back to her for 150 x 0.6 = $90. She then sold it to Charlie for 90 x 1.3 = $117. In the first transaction (with Ben), Annie made $50 (on $100), and in the second transaction (with Charlie), she made $27 (on $90). Therefore, her overall profit percentage is;

(50 + 27)/(100 + 90) = 77/190 ≈ 0.4053 = 40.53%

Answer: A

Divyanshu14 · Answer

Isn't the question asking overall Profit%? Ideally it should be Total Profit/Total CP=40.53%

Nikkz99 · Answer

Bunuel   Krunaal 
I went with Option A and that only sounds logically correct according to the question it framed. 
Also, do these kinds of questions come during the GMAT exams?

Thank you

princevora · Answer

lets say you start day trading with $100 and in a month you have $177 in your trading account. what is the profit percentage. I think it's a very similar situation to above. so profit should be calculated on initial investment rather then turnover/sales.

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