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# A store sold a TV at a price three times as much as a DVD

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Director
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A store sold a TV at a price three times as much as a DVD [#permalink]

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19 Feb 2004, 23:37
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A store sold a TV at a price three times as much as a DVD player.
The gross profit of TV is 80% of the price that the store paid for it.
The gross profit for DVD player is 20% of the price that the store paid for it.
What percent is the total gross profit of the total amount that the store paid for both the items?

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Senior Manager
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19 Feb 2004, 23:47
Let 'T' be the cost of the TV and 'D' be the cost of the DVD. From the statement we know that T=3D (TV= 3 times DVD).

And also the profit for TV is 80% more that is sold for 1.8 times T
Similarly for DVD is 20& that makes 1.2 times D

The % calculation is (1.8T+1.2D)/(T+D) ===>>>

Sunstituiting T=3D, we get 6.6D/4D and in % wise it is 128%.
Is it correct?.

Or is it that the gross profit comes to 0.8T+0.2D which is 2.6D (substituiting T=3D)... therefore 2.6D/4D is equal to 65%.

Which is correct.

Regards
Carsen

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Director
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20 Feb 2004, 03:13
Think that it is 60%. 1) Ptv=3Pdvd, Ptv=0.8Ctv+Ctv=1,8Ctv, where C is the price paid by the shop for the TV. For the DVD, Pdvd=0,2Cdvd+Cdvd=1.2Cdvd. When we substitute in 1) then 1,8Ctv=3,6Cdvd or Ctv/Cdvd=2 or the shop paid twice as much for a TV set as for a DVD. or Ctv=2Cdvd and 0,2Cdvd+0.8Ctv/3Cdvd=
0.2Cdvd+0.8x(2Cdvd)/3Cdvd=1,8Cdvd/3Cdvd=60%

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SVP
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20 Feb 2004, 09:14
Hi BG,

I never knew what a Brain dump is. Your analysis shows what it can be.
You have a real good consistency in reaching the end point. People can easily get lost in the jungle of equations. If you did this in under 2 minutes I shall bow in front of you

Anand.

Let TV cost \$100 then the selling price = \$180 ( for 80% profit )
Since Selling price of TV \$180, selling price of DVD player = \$60
Since profit on DVD player if 20% cost of DVD = \$60/1.2 = \$50

Total revenue from sale = 180+60 =\$ 240
Total cost = \$150
Profit = 240-150 = \$90
%profit = 90/150 * 100 = 60%

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Senior Manager
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20 Feb 2004, 11:31
Let 'T' be the cost of the TV and 'D' be the cost of the DVD. From the statement we know that T=3D (TV= 3 times DVD).

Selling price for TV = 1.8 T
Selling price of DVD is 1.2 D

Total Selling price = 1.8T + 1.2D = 6.6 D by substituting T = 3D

Total Cost price = T+D = 4D by substituting T = 3D

Profit = SP-CP = 6.6D-4D = 2.6D
% Profit = 2.6D/4D *100 = 65 %!!

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Director
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20 Feb 2004, 12:21
cbrf3 wrote:
Let 'T' be the cost of the TV and 'D' be the cost of the DVD. From the statement we know that T=3D (TV= 3 times DVD).

A store sold a TV at a price three times as much as a DVD player.
It is not T=3D, but S(T) = 3S(D); in other words
(1.8 T) = 3 * (1.2 D).

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Senior Manager
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20 Feb 2004, 12:31

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Senior Manager
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20 Feb 2004, 12:39
65%

Let the price of TV = X
Let the price of DVD = Y
Let profit for TV = Ptv
Let profit for DVD = Pdvd

X = 3Y
Ptv = 4/5(X) = 4/5(3Y) = 12/5Y
Pdvd = 1/5Y

Total amount paid = 3Y + Y = 4Y
Total profit = 12/5Y + 1/5 Y = 13/5Y
% of total gross profit of the total amount = (13/5Y)/4Y = 13/20 = 65%

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Director
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20 Feb 2004, 13:14
ndidi204 wrote:
% of total gross profit of the total amount = (13/5Y)/4Y = 13/20 = 65%

What has been asked is the profit/cost not profit/(sale price).
If you calulcate the profit/cost it is 60%

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Manager
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23 Feb 2004, 16:41
60%

on questions like this I go with picking numbers

let DVD cost 100
profit 20
sell 120

TV sell 120*3 = 360
Cost x
1.8x = 360 (80% profit) X=200
profit = 160

Total profit = 180
total cost = 300

Ans: 60%

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23 Feb 2004, 16:41
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