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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 55% (02:35) correct 45% (02:52) wrong based on 112 sessions

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Q. 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

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  _________________
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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

Originally posted by EgmatQuantExpert on 25 Apr 2017, 00:43.
Last edited by EgmatQuantExpert on 30 Apr 2017, 01:29, edited 1 time in total.
Senior Manager  G
Joined: 19 Apr 2016
Posts: 268
Location: India
GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5
WE: Web Development (Computer Software)
Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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EgmatQuantExpert wrote:
Q. 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

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  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 Intern  B Joined: 18 Jul 2016 Posts: 16 Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 1 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 _________________ Engineer, Quant score 53 First attempt. Manager  S Joined: 25 Apr 2016 Posts: 59 Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 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 e-GMAT Representative V Joined: 04 Jan 2015 Posts: 3078 Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 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  _________________ e-GMAT Representative V Joined: 04 Jan 2015 Posts: 3078 Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 1 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  _________________ Manager  S Joined: 10 Apr 2015 Posts: 177 GPA: 3.31 Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 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. _________________ In case you find my posts helpful, give me Kudos. Thank you. Intern  B Joined: 14 May 2015 Posts: 47 Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 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 Manager  G Joined: 14 Jun 2018 Posts: 217 Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 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 GMAT Club Legend  D Joined: 18 Aug 2017 Posts: 5027 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If [#permalink] Show Tags 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 ; $8 IMO A EgmatQuantExpert wrote: Q. George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If he makes a net profit of 10% on this transaction and the selling price of CDs is$ 36, find the selling price of DVDs.

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

Thanks,
Saquib
Quant Expert
e-GMAT

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   Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If   [#permalink] 23 Aug 2019, 09:32
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