Tom can paint the fence either with blue or red paint. Blue paint cost

Question

Tom can paint the fence either with blue or red paint. Blue paint costs 50% more per liter than red paint. However, blue paint covers 20% more area per liter than red. What percent less is the cost per square meter when using red paint compared to blue paint?

A. 10%
B. 15%
C. 20%
D. 25%
E. 30%

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Bunuel · Accepted Answer

Official Solution:

Tom can paint the fence either with blue or red paint. Blue paint costs 50% more per liter than red paint. However, blue paint covers 20% more area per liter than red. What percent less is the cost per square meter when using red paint compared to blue paint?

A. 10%
B. 15%
C. 20%
D. 25%
E. 30%

Assume the cost per liter of red paint is  $100 , and 1 liter covers 100 square meters, making the cost per square meter for red paint  \frac{$100}{100}=$1 , or 100 cents.

Then, for blue paint, the cost per liter would be  $100 * 1.5 = $150 , and 1 liter would cover  100 * 1.2 = 120  square meters, making the cost per square meter for blue paint  \frac{$150}{120}=$1.25 , or 125 cents.

Hence, the cost per square meter when using red paint compared to blue paint would be:

\frac{	ext{the cost per square meter for blue paint} - 	ext{the cost per square meter for red paint}}{	ext{the cost per square meter for blue paint}} * 100 = \frac{125 - 100}{125} * 100 = 20  percent less.

Answer: C

Purnank · Answer

Lets assume 100 units as cost of red paint and blue paint costs 50% more per liter than red paint.
Therefore, Cost of blue = 150 units/liter,
and assume 10 Sq m area red paint covers per liter, Also blue paint covers 20% more area per liter than red.
Therefore Area covred by blue paint = 12 Sq m/lit
So for covering 10 units area with blue paint the cost will be required = 10 * 150 / 12 = 125 units/sq m
But with red paint for same area cost is 100 units/sq m
Therefore, Percent less is the cost per square meter when using red paint compared to blue paint = (125 - 100) * 100 / 125
=20%
I think answer is C.

tgsankar10 · Answer

Cost per sq.m = Price per litre/Area covered per litre

Cr=\frac{Pr}{Ar}

Cb=\frac{Pb}{Ab}

Pb=1.5Pr  (50% more price/litre)

Ab=1.2Ar  (20% more area coverage/litre)

Cb=\frac{1.5*Pr}{1.2*Ar}

Cb=1.25Cr

Cr=0.8Cb

Cost per sq.m of using red paint is  20%  less than using blue paint

Answer is C

Nidzo · Answer

Let the price of the red paint be  x , which means that the price of the blue paint is  1.5x 
Let the area that the red paint can cover be  y , which makes the area the blue paint can cover equal  1.2y

Red Price/Area:   \frac{x}{y}

Blue Price/Area:   \frac{1.5x}{1.2y}

What percent less is the cost per square meter when using red paint compared to blue paint:

\frac{\frac{1.5x}{1.2y}-\frac{x}{y}}{\frac{1.5x}{1.2y}}*100

\frac{0.3x}{1.2y}*\frac{1.2y}{1.5x}*100

\frac{30}{1.5}

20

ANSWER C

Dheeraj_079 · Answer

Let the cost of Red paint per liter be x and the volume of paint required be y.
Cost of using red paint = xy

Cost of Blue paint per liter is x * 1.5 and the volume of paint required is y / 1.2

Cost of using blue paint = 1.5x * y/1.2 = 5xy/4

Percentage decrease of using red paint instead of blue = (5xy/4 - xy) / (5xy/4)*100
                                                                               = 20%
The answer is C

KarishmaB · Answer

When we have a product of two terms, it is similar to successive percentage changes.

Expense for a unit area = Price * Amount used

For blue paint, price is 50% more i.e. 3/2 of the price of red paint
Since blue paint covers 20% more area i.e. 6/5 area, the amount of paint used is 5/6 of the amount of red paint used

Expense for a unit area of Blue paint = 3/2 * Price * 5/6 * Amount used = 5/4 * Expense for a unit area of red paint

Expense for a unit area of red paint = 4/5 * Expense for a unit area of Blue paint

i.e. red paint is 20% cheaper per square meter.

Answer (C)

Here is the discussion on multipliers for percentages:  https://youtu.be/HxnsYI1Rws8

Tom can paint the fence either with blue or red paint. Blue paint cost

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Tom can paint the fence either with blue or red paint. Blue paint cost

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