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An artist who needs to buy only paint and canvas finds that the cost

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Bunuel
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An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   16 Nov 2015, 03:16
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An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?

A. 40%
B. 44%
C. 50%
D. 56%
E. 60%
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D
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longfellow
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Re: An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   16 Nov 2015, 06:14
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Answer is 56

let canvas=10 and paint=40
total=50

new price will be
canvas=6 and paint=16
total=22

Decrease of 28
%= 28/50 *100=56
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KarishmaB
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An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   24 Nov 2021, 01:30
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Bunuel wrote:
An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?

A. 40%
B. 44%
C. 50%
D. 56%
E. 60%


Using our weighted average formula,

\(\frac{1}{4} = \frac{-60 - Cavg}{Cavg - (-40)}\)
\(Cavg = - 56 \)

Answer (D)
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KarishmaB
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Re: An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   26 Dec 2023, 04:10
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shivanks wrote:
longfellow wrote:
Answer is 56

let canvas=10 and paint=40
total=50

new price will be
canvas=6 and paint=16
total=22

Decrease of 28
%= 28/50 *100=56

can you please explain how new price will be 6 or 16 after discount?
60% on 10 rs then new price must be 4 rs ? please explain me how it can u 6 where i'm missing.


Discount on canvas is 40% so $10 of canvas becomes 40% reduced and becomes $6.
Discount on paints is 60% so $40 of paint becomes 60% reduced and becomes $16 (Do this orally - 50% of 40 is 20. 10% of 40 is 4. So overall 60% reduction means a reduction of 20 and 4 i.e. a reduction of 24 which means $40 becomes $16.

Check this YouTube video that discusses these calculations: https://youtube.com/shorts/ik20fyTFlL0
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HardWorkBeatsAll
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Re: An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   16 Nov 2015, 04:08
Paint:Canvas cost is 4:1.

So, paint accounts for 80% of cost and canvas accounts for 20%.

Canvas, after decrease by 40% will be (100-40)% of 20% => 60% of 20% => 12% of original
Paint, after decrease by 60% will be (100-60)% of 80% => 40% of 80% => 32% of original

New cost as a % of old cost = 32+12 = 44% of original.
So, overall cost saving = 100-44 = 56%

Therefore, (D)

Bunuel wrote:
An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?

A. 40%
B. 44%
C. 50%
D. 56%
E. 60%
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Re: An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   17 May 2016, 12:03
Bunuel wrote:
An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?

A. 40%
B. 44%
C. 50%
D. 56%
E. 60%

Earlier P=4C
so cost of buying both =5C (C+4C)
present discounted price=C(1-40/100) + P(1-60/100)
=3C/5+2P/5
as P=4C------>total price 3C/5+8C/5----11C/5
% change=(5C-11C/5)/5C----->14/25-----56%
Ans D
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TomNook
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An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   23 Nov 2021, 18:27
Bunuel wrote:
An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?

A. 40%
B. 44%
C. 50%
D. 56%
E. 60%


Let C represent the original cost of canvas
Let P represent the original cost of paint
Let X represent the original total cost
Let Y represent the new total after discounts for canvas and paint

\(P = 4C\)

\(X = 4C + C\)

\(Y = 0.6C+0.4P\)

% decrease = \(\frac{X - Y }{ X} * 100\)

% decrease = \(\frac{(4C+C)-(0.6C+0.4*(4C))}{(4C+C)} * 100 \)

% decrease = \(\frac{5C-2.2C}{5C} * 100 \)

% decrease = \(\frac{2.8}{5} * 100\)

% decrease = 56%

Thus answer is D
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Re: An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   25 Dec 2023, 21:20
longfellow wrote:
Answer is 56

let canvas=10 and paint=40
total=50

new price will be
canvas=6 and paint=16
total=22

Decrease of 28
%= 28/50 *100=56

can you please explain how new price will be 6 or 16 after discount?
60% on 10 rs then new price must be 4 rs ? please explain me how it can u 6 where i'm missing.
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GMATGuruNY
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Re: An artist who needs to buy only paint and canvas finds that the cost [#permalink] New post   25 Dec 2023, 21:52
Expert Reply
Bunuel wrote:
An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?

A. 40%
B. 44%
C. 50%
D. 56%
E. 60%


paint:canvas = 4:1
paint decreases in cost by 60%, canvas decreases in cost by 40%
Thus:
For every 4 units of paint decreasing in cost by 60%, 1 unit of canvas decreases in cost by 40%.
Average decrease in cost for every 5 units \(= \frac{(4*60) + (1*40)}{5} = 56\)

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Re: An artist who needs to buy only paint and canvas finds that the cost [#permalink]
25 Dec 2023, 21:52
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