A trader marks-up his goods by 30% and then offers a discount of 10%.

Question

A trader marks-up his goods by 30% and then offers a discount of 10%. Find the net profit or loss percentage that he makes.

1. 15
2. 17
3. 20
4. 25
5.30

GmatPrime · Answer

Let the cost price be x

Mark-up by 30%
So the resulting Price= 1.3x

Now, discounts 10% 
Therefore, remaining price = 90% of 1.3x = 0.9*1.3x = 1.17x

That is, % increase = 17%

Answer is B

LeoN88 · Answer

CP 100
Marked to 130
Final SP after Discount= 130* (9/10) = 117

Gain% is 17

alexx2 · Answer

If a retailer marks up his goods by 30% and then offers a discount of 10%, what is his profit%?

A 10%
B 3%
C 17%
D 20%
E 40%

GMATin · Answer

This is more likely a sub-600 level question. Explanation below:

Let's assume the goods to be priced at 100. Mark up of 30% on 100 gives us 130 as the marked up price. A discount of 10% on 130 reduces the price by 13 which gives us 117. Now 117 is 17% up from the original price of 100. This is the profit%.

AndrewN · Answer

Key points : Before we get into solving the problem, we need to know what to focus on, and here, the question is pretty clear: the  profit  (by percentage).
 Answers : A glance down the answer column tells us that the percentage dips after choice (A) but then increases from choice to choice thereafter.
 Breakdown : Many times when I deal with percentage problems, I prefer to use numbers instead of algebra, since I feel more comfortable with numbers and find that I make fewer mistakes. Since  percentages are based on 100 , I would set the value of the goods the retailer is selling at $100. Thus, marking up those goods by 30 percent would be equivalent to increasing the price by $30. With that part out of the way, a discount of 10 percent needs to be applied to  the new number , NOT the initial $100. Using the  10% rule , in which we can instantly determine 10 percent of a number by pushing the decimal one place to the left, we can see that 10 percent of $130 would be $13. All that remains is a little subtraction to yield the profit:

$130 - $13 = $117 and
$117 - $100 (our baseline) = $17

This number represents the percent profit, and choice (C) is the answer.

Another approach : Algebra can come in just as handy here, but such a method requires knowledge or experience of decimals as they relate to percentages. If we take the cost of the goods as C, then we could think of that amount as representing 100 percent of C, or 1.00C. Increasing this amount by 30 percent, or 0.30C, would yield

1.00C + 0.30C, or 1.30C

At this point, we could apply the discount of 10 percent in the same manner we had before, as in

(0.10)(1.30C) = 0.13C

Subtracting this amount from the marked-up price would give us 1.30C - 0.13C, or 1.17C. Finally, the difference between 1.17C and 1.00C is 0.17C, the profit margin. It looks like (C) wins again.

A third approach : To streamline the problem, we could just apply the discount to 100 - 10, or 90 percent of the increased price and multiply through to get the answer:

(1.30C)(0.90) = 1.17C

As the old saying goes, there is more than one way to skin a cat.

A fourth approach : It is okay to assume that an answer is correct and work backwards from there to check for validity. Some problems lend themselves to such a method better than others, but it can be done with this one. Let us assume that the answer is (D), 20%, since I imagine most people would intuitively pick this answer. Combining, say, the first approach with this one, start with $100 and then kick it up to $130 to reflect the markup. If 20 percent is the answer, then the profit  must be  $20. The question then becomes, is $120 equivalent to 10 percent off $130? In a word, no. 90 percent of 130 is, of course, 117, and 120 ≠ 117.

Other answers :

(A) 10%

Analysis: This looks to be nothing more than a  convenient  answer, lifted straight from the problem itself. I would imagine few test-takers picking it, with an  increase  of 30 percent and a  decrease  of 10 percent staring them in the face. Red light.

(B) 3%

Analysis: There is a tenuous connection to the problem, namely 30 divided by 10, but the reason for why we would divide the two given numbers is a mystery. Red light.

(D) 20%

Analysis: Ah, the trick answer, the one I imagine many inexperienced test-takers choosing, following the logic that if something increases by 30 and then decreases by 10, the net change would be +20. Of course, as outlined above, that would be ignoring the fact that the discount should be taken off the increased price, rather than the original cost. Be careful. Yellow light.

(E) 40%

Analysis: For someone truly in a hurry, adding 30 percent and 10 percent would get 40 percent, but again, not only does the logic make no sense, with the former number representing an increase and the latter a decrease, but 1-2 (i.e. simple) combinations of given numbers so rarely prove to be correct. Mark this one as another  convenient  answer and move on. Red light.

Guessing : The only reasonable answers, given one increase in a percent and a decrease in another, are choices (C) and (D), for reasons explained above. Whether you choose to solve the question via numbers, algebra, or logic--perhaps thinking,  I know this 20 is a trap, so it must be the other one --getting past this 50/50 should not prove too difficult.

I hope this helps anyone who may have blundered into (D). Happy studies.

MahmoudFawzy · Answer

Effective Percentage Change is an important formula to know, and helps in GMAT.
 https://gmatclub.com/forum/percentages-interest-and-more-208098.html#p1596558

effective percentage =  x + y + \frac{xy}{100} 
in our case,  x = 30 , and  y = -10  -------> then  x + y + \frac{xy}{100}  =  30 - 10 - \frac{300}{100} = 17 
  C

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A trader marks-up his goods by 30% and then offers a discount of 10%.

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