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

Question

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%

HardWorkBeatsAll · Answer

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)

longfellow · Answer

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

rohit8865 · Answer

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

TomNook · Answer

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

KarishmaB · Answer

Using our weighted average formula,

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

Answer (D)

shivanks · Answer

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.

GMATGuruNY · Answer

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

D

KarishmaB · Answer

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

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