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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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George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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24 Apr 2017, 23:43
1
8
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Difficulty:

85% (hard)

Question Stats:

54% (01:59) correct 46% (02:43) wrong based on 117 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

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George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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Updated on: 30 Apr 2017, 00:29
The official solution has been posted. Looking forward to a healthy discussion..
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Originally posted by EgmatQuantExpert on 24 Apr 2017, 23:43.
Last edited by EgmatQuantExpert on 30 Apr 2017, 00:29, edited 1 time in total.
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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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25 Apr 2017, 00:01
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

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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
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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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25 Apr 2017, 00:07
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
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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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25 Apr 2017, 00:21
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
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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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30 Apr 2017, 00:27

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
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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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30 Apr 2017, 00:36
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
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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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30 Apr 2017, 10:59
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.

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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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03 May 2017, 13:55
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
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Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If  [#permalink]

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20 Oct 2018, 11:46
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
Re: George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If &nbs [#permalink] 20 Oct 2018, 11:46
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