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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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New post 24 Apr 2017, 23:43
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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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New post 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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New post 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
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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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New post 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
Hence answer is 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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New post 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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New post 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.


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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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New post 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, \(SP = 4 * \frac{30}{15} = $8\)


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Saquib
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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
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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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New post 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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New post 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
answer: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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New post 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
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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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