George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If

Question

George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If he makes a net profit of 10% on this transaction and the selling price of CDs is $ 36, find the selling price of DVDs.

A. $8
B. $10
C. $20
D. $25
E. $30

Thanks,
Saquib
Quant Expert
e-GMAT

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EgmatQuantExpert · Answer

The official solution has been posted. Looking forward to a healthy discussion..

0akshay0 · Answer

original CD price = 36/1.2 = 30 36 + 0.80*DVD_price = (DVD_price + CD_price)*1.10 36 + 0.80*DVD_price = (DVD_price + 30)*1.10 36 + 0.8*DVD_price = 1.10*DVD_price + 33 3 = 0.3*DVD_price DVD_price = 10 Selling Price of DVD = 0.8*10 = $8 Hence option A is correct Hit Kudos if you liked it 8-)

skothaka · Answer

Cost Price of CD and DVD are C and D respectively
Selling Price of CD and DVD are 1.2C and 0.8D respectively
given 1.2C=36, means C=30

total profit = total Selling price/total Cost price - 1 = 0.1 (here 0.1 means 10%)
So,
1.1 = (1.2C + 0.8D)/(C+D)
1.2C + 0.8D = 1.1C + 1.1D
0.1C = 0.3D
we know C=30
so , D= (0.1*30)/0.3 = 10
So selling price is 0.8D = 8
Hence answer is A

attari92 · Answer

cost price of CD = 5/6* 36 =30
Now, as per question ratio of the cost price of CD's to the cost price of DVD's would be 3:1 and 3 implies 30, which means 1 part corresponds to 10. Given, DVD's loss percent =20% => SP of DVD's = 10*4/5 =8 => option A

EgmatQuantExpert · Answer

Solution Given: • Profit % on CDs = 20 % • Loss % on DVDs = 20 % • Overall Profit = 10 % • Selling Price of CDs = $ 36 Working: • Cost Price of CDs * (1 + \frac{1}{5}) = $ 36 • Cost Price of CDs = $ 30 • Let the Cost Price of DVDs = D o Loss on DVDs = -D*\frac{1}{5} = -\frac{D}{5} • Overall Profit = (36-30) + \frac{D}{5} = 6 - \frac{D}{5} • % Profit = (6 - \frac{D}{5})/(D+30) • \frac{(30 - D)}{5(D+30)} = \frac{1}{10} • 60 - 2D = D + 30 • D = 10 • Note: We have been asked the SP of DVDs, so don’t mark Option B as you answer, otherwise all the hard work will be a BIG waste. • SP of DVDs = 10( 1-\frac{1}{5}) = $ 8 • Hence the correct answer is Option A . Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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EgmatQuantExpert · Answer

Method 2 • Let CP of CDs be C and CP of DVDs be D . • Thus, we can write o (Profit from C – Loss from D)= Overall Profit*(Sum of CP of C and D) o (C*\frac{1}{5} – D*\frac{1}{5}) = \frac{1}{10}*(C+D) o \frac{(C-D)}{(C+D)} = \frac{1}{5} o D = \frac{C}{3} • We need to find the SP of DVDs = D*(1-\frac{1}{5}) = \frac{4D}{5} o As D = \frac{C}{3} o SP of DVDs = \frac{4D}{5} = \frac{4C}{15} • Cost Price of CDs * (1 + \frac{1}{5}) = $ 36 • Cost Price of CDs = $ 30 • Thus, SP = 4 * \frac{30}{15} = $8 Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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shekyonline · Answer

y- actual price of DVD.

36+ 0.8y = (30 + y) * 1.1 
0.3y = 3
y = 10

Selling price of DVD- 0.8 y = 8 .

Ans A.

ishaan.wares · Answer

Cp of cd=36/1.2=30
cp of dvd=x
sp of dvd=0.8x
atq
(0.8x+36)-(x+30)=(x+30)0.10
solving, x=10
sp of dvd=10*0.8=8
answer:A

pandeyashwin · Answer

Let x & y be the cost of Cd and DVD respectively.
1.2x + 0.8y = 1.1x + 1.1y
x = 3y
Given , 1.2x = 36 ; x= 30
Therefore , y = 10 and selling price of dvd = 80% of 10 = 8

Archit3110 · Answer

CP of Cd; 36/1.2 ; 30$
so x be the CP of dvd
36+0.8x=(x+30)*1.1
solve for x ; 10
SP of DVD ; 10*.8 ; $8
IMO A

Ved22 · Answer

This question can be solved within 3 mins a single concept of weighted avg

Kinshook · Answer

Given: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%.
Asked: If he makes a net profit of 10% on this transaction and the selling price of CDs is $ 36, find the selling price of DVDs.

Selling price of CD = $36
Cost price of CD = $36/1.2 = $30

Let the selling price of DVDs be x.
Cost price of DVDs = x/.8 = 1.25x

Total cost price = $30 + 1.25x
Total selling price = $36 + x = 1.1 ($30 + 1.25x) = $33 + (11/10)*(5/4)x = $33 + 11x/8
3x/8 = $3
x = $8

IMO A

Rutvik01 · Answer

Can it be solved faster?

sayan640 · Answer

gmatophobia , can you please solve it using alligation diagram/weighted avg. ?

sayan640 · Answer

From the alligation diagram we can find out that the c.p of CD and DVD are 3:1 ratio.
The cp of CD = say X
1.2 X = 36
X= 30
Note: Profit is calculated in terms of Cost prices . Hence the alligation diagram gave us the ratio of cost prices. Please find it attached .

Then the CP of DVD = 10..
The S.P of DVD = .8 * 10 = 8

A is the answer.  egmat   gmatophobia   KarishmaB

PocusFocus · Answer

I have a doubt here, I noticed that margins are calculated taking cost as the base, but I've been working in finance several year and I've never see calculate margins that way, margins are calculated taking sales as the base, so for instance:

"George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If he makes a net profit of 10% on this transaction and the selling price of CDs is $ 36, find the selling price of DVDs."

If the selling price of the CD is $36 and the profit is 20% the cost is 80% x 36 = 28.8

Is different in GMAT or I missing something in the text? Please your help.

egmat · Answer

PocusFocus  You've identified exactly the right issue: in corporate finance, "margin" is typically calculated on  sales  (revenue), but in GMAT problems (and standard mathematics), profit and loss percentages are  always  calculated on the  cost price  as the base, unless explicitly stated otherwise.

You can also confirm this by testing your approach:

Let's test your approach:
 
 If SP =  $36  and you calculate CP as  80\%  of SP: CP =  0.8 	imes 36 = $28.80  
 Now verify: If CP =  $28.80  and we add  20\%  profit: SP =  28.80 	imes 1.2 = $34.56  
 But we know SP =  $36 , not  $34.56  – contradiction!

This confirms that the  20\%  profit is calculated on the  cost , not the selling price.

Strategic Tip for Future Problems

GMAT Convention:  Profit/loss percentages are  always cost-based  unless you see explicit language like "margin as a percentage of sales" or "profit on selling price." This wording is extremely rare on the GMAT. When you see "profit of  20\% " – think  SP = 1.2 	imes CP  automatically.

George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If

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George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If

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