In order to give his customers a 25-percent discount on the price and

Question

In order to give his customers a  25-percent  discount on the price and still net a  25-percent  profit on the cost of an item, at what price should a merchant mark an item if it cost him  $16.80 ?

(A)  $21.00 
(B)  $21.90 
(C)  $25.20 
(D)  $26.25 
(E)  $28.00

AaronPond · Accepted Answer

Let's talk strategy here. It looks like many of the approaches in this forum focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to use strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The "GMAT Jujitsu" I will show you here will be useful for numerous questions, not just this one. My solution here is going to walk through not just what the answer is, but how to strategically think about it.

Let's start with breaking down the original question. We know that the the cost of the item is  $16.80 . We also know that   Profit = Revenue - Cost  . If the merchant wants to have a profit of 25% of the cost, that means that the revenue (the price he actually charged for the item) must be   1.25*Cost  . After all,   Profit = 1.25*Cost - Cost = .25*Cost  . Note that this part of the problem is not a percentage change issue, but it looks a little like one, because in the end you are looking for Revenue. In order for Profit to be 25% of Cost, then the Revenue must be 125% "of" cost. Our leverage from here on out, however, is the revenue ( $16.80*1.25 ), since this is the amount of money the merchant receives.

Here is where the first strategic approach comes in. I call it in my classes "  Fractions Are Your Friends  ." Many math questions are made easier if you can think of decimals in terms of their corresponding fractional equivalents. Decimal multiplication and division -- while useful -- are often the long way around when it comes to math. It should be easy to see that  1.25 = \frac{5}{4} . Thus,

Price_{(Actual)}=$16.80*1.25=$16.80(\frac{5}{4} )

You should be able to see how quickly we can divide  $16.80  by  4 , and then multiply by  5 . If you use the fractions and break up math into easier-to-digest parts, the math is doable in your head. This is not accidental. The GMAT often designs problems so that the math is easy for those that know how to   think   about the problems. For purposes of visualization, here is what it looks like:

16.80*\frac{5}{4}=(\frac{(16+.80)}{4})*5=(4+.2)*5=20+1=21

The actual price is  $21 .

Now, this price is the what the merchant is  actually  charging his customers. This, however, is the   already-discounted   price. The target of this question is the price at which the original item was marked. A discount is a percentage change, so we can use the formula  V_{(final)}=V_{(initial)}*(1\pm(\frac{\%}{100})) . In the case of this question, our actual price is the final value,  V_{(final)} . Our initial value,  V_{(initial)} , is what the merchant originally wanted to charge. Using "  Fractions Are Your Friends  " again, we get:

V_{(final)}=V_{(initial)}*(1\pm(\frac{\%}{100}))  
  $21=	ext{Price}_{(initial)}*(1-(\frac{25}{100}))  
  $21=	ext{Price}_{(initial)}*(1-\frac{1}{4})  
  $21=	ext{Price}_{(initial)}*(\frac{3}{4})  
  	ext{Price}_{(initial)}=21*(\frac{4}{3})=$28

Again, notice how easy it is if you keep the numbers in fractions.  $21*1.3333  is messy. But cancelling out the factor of  3  from  21  (leaving  7*4  in the numerator) is a piece of proverbial cake.

The answer, therefore, is  E .

rohit8865 · Answer

so finally he should have 25% profit over $16.8 which is 16.8(1+25/100)= $21
but this $21 is discounted price of SP say x at 25%
again x(1-25/100) = 21
thus x=$28

Ans E

Abhishek009 · Answer

Cost Price + Profit = Selling Price = Marked Price - Discount

Now, here Selling Price will be 16.80*125/100 = 21

Now, at this point we have here , Selling Price which is 75% of Marked Price...

So, Marked Price = 21/0.75

Or, Marked Price = 28.00
  
Hence Correct answer must be (E) 28

lovenish · Answer

In order to give his customers a 25−percent25−percent discount on the price and still net a 25−percent25−percent profit on the cost of an item, at what price should a merchant mark an item if it cost him $16.80?

(A) $21.00
(B) $21.90
(C) $25.20
(D) $26.25
(E) $28.00

Do it in steps:

Given: Cost price : $16.80

Final result to achieve is  "to gain 25%" of cost price

so keeping end result in mind find the 25% of Cost price = $16.80*(25/100) =$16.80 *(1/4) = $4.20

Now add the profit in the cost price=$16.80+$4.20= $21.00

Now you should  use the options   that is when you apply discount of 25% on any of the option and if it gives you $21.00 as a result  then it is your answer:

if you give the discount of 25 % on $28.00=  $28.00 - $28.00 (25/100)  = $28.00 -$7.00 =  $21.00

So the Answer is  E

Andruida · Answer

According to the question:
 (1-0.25)P = (1+0.25) * 16.8

herefore P = 28.00

Mo2men · Answer

Hi AaronPond Thanks for your great explanation

Can you please shed light about the meaning of mark price, mark up and mark down? What kind of relationship with revenue or price? Thanks in advance

Antreev · Answer

So basically we have a cost price first to which a % of margin is added to reach the marked price. This margin is added so as to leave some room for discount and still earn profit. 
After the Marked price , some discount is given and the product is sold at selling price or marked down price. When we subtract cost price from this selling price we get Profit.

so if CP is 100 Rs
MP is 130 Rs (30% up the CP)

a discount of 10% on MP is given i.e Rs 13
so SP - 117
Profit - Rs 17 or 17%

Posted from my mobile device

eabhgoy · Answer

We need to apply a profit of 25%:

Intermediate Price = 125% of 16.8 = (5/4) * 16.8

Also give a 25% discount on the selling price:

75% of selling price = intermediate price

(3/4) * SP = (5/4)*16.8

=> SP = (16.8 * 5)/3 = 84/3 = 28

Hence E is the correct answer

Henry S. Hudson Jr. · Answer

cost(1+p/100)=Marked Price (1-d/100)

16.80(1+25/100)=M(1-25/100)

16.80(1.25)=.75M

/.75=M

28=m

prabsahi · Answer

let cost be c and marked price be 'm' then .75% of C= 125% of M implies 3/4* c=5/4 *m implis 3C=5M now put value of C as 16.8 s we get M=28

Zishanuddin · Answer

Lets go easy!
Here shopkeeper wants 25% profit right. Then 25%of 16.80 will be 4.20

Add 16.80 + 4.20 = 21.

Here 21 is the price after a discount of 25% as per question. Then 21 must be 75% of total price.

From above we can find the rest 25 percent and add to the 21.

21 + 7 = 28 ans

Posted from my mobile device

fireagablast · Answer

Still working on getting the hang of translating these problems, but here's my solution.
We have:
1. Purchase cost
2. Original Sell price
3. New Discount price
4. Profit margin
5. Final sell price

Purchase cost = $16.80
Original Sell price = x
New discount price = -25% = x*(75/100)
Profit Margin = +25% = 125/100
Final sell price = 16.80*(125/100)

75x/100 = 16.80*125/100
x=28

ThatDudeKnows · Answer

Two ways.

First, Pieces of the Puzzle
Cost $16.80. Need a 25% profit. 25% of $16.80 is $4.20. Have to sell for $21. What price do we need to mark it at in order to discount by 25% of that number and still sell for $21? $28.
Answer choice E.

Second, Plugging In The Answers (PITA)
I like trying B and D. 
B: Discount $21.90 by 25%...we're going to be cutting off more than $5. We won't even be selling for more than we paid, so we certainly won't be making 25% profit! No need to continue with B, and A is also eliminated. Down to C, D, and E.
D: We can't take 25% off from $26.25 and end up with a whole number of cents. D is wrong. Down to C and E. E looks easier to work with.
E: $28. Discount by 25%. 25% is $7. Sale price is $21. Profit is $4.20. Is that 25% of $16.80? Yep.
Answer choice E.

adityasuresh · Answer

In order to give his customers a 25−percent discount on the price and still net a 25−percent profit on the cost of an item, at what price should a merchant mark an item if it cost him $16.80?

(A) $21.00
(B) $21.90
(C) $25.20
(D) $26.25
(E) $28.00

( 1+m/100 )∗( 1−d/100 )=( 1+p/100 )
where m% is mark up %, d% is discount % and p% is profit %.

(1 +  M/100 )*(1- 25/100 ) = (1+ 1/4 )
(1 +  M/100 ) *  3/4  =  5/4 
1 + M/100 =  5/4  *  4/3 
 M/100  =  5/3  -1
M =  2/3  * 100
This implies mark up % =  200/3 
Mark up price = CP +  2/3  CP
OR  5/3  CP =  5/3  * 16.8 = 28

E

BLTN · Answer

Profit = Revenue - Cost 
  \frac{ 1}{4}*C= R*\frac{3}{4 }- C   
  \frac{ C}{R}= \frac{3}{5 }

Substitute 16.8 for cost 
  \frac{ 16.8}{R}= \frac{3}{5 }  
 R = 28

TargetMBA007 · Answer

I did this using the

(1+m/100)(1-d/100) = (1+p/100) approach, which gave me a 66% mark-up and then in step 2, I marked up the cost by 66% to arrive at the correct answer.
But I just wondered, if the formula can be adjusted, to make this a one-step process.

KarishmaB

KarishmaB · Answer

Look, the formula is basically a multiplication of Multipliers. Cost Price * Mark Up Multiplier * Discount Multiplier = Selling Price = Cost Price * Profit Multiplier You need the value of "Cost Price * Mark Up Multiplier" as the answer. But Cost Price gets cancelled and I get Mark Up Multiplier * Discount Multiplier = Profit Multiplier I am given that the "Discount Multiplier" = 3/4 and "Profit Multiplier" = 5/4 So "Mark Up Multiplier" is simply 5/3. To get Marked Price, all you have to do now is multiply it with cost price i.e. Cost Price * Mark Up Multiplier = 16.8 * (5/3) = $28 Answer (E) Here is a discussion on fraction percent equivalents: https://youtu.be/HxnsYI1Rws8

Jaival · Answer

Discount of 25% on selling=3/4 of Selling price
Nowq this should get a profit of 25%=5/4 Of CP
Given CP=16.8 We get 5/4.CP=21
Now this 21=3/4(S.P.)
21=3/4.SP
SP=21 x 4/3
=7x4
=28

chattyyee · Answer

Is it just me or the - percent came off really confusing, and I kept trying to solve it as 25-percent as percent being some variable?

In order to give his customers a 25-percent discount on the price and

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