M39-78

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%

Show Answer

Official Answer

C

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

Bunuel · 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%

Show Answer

Official Answer

C

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

AaryanGupta1200 · Answer

This is a great question that’s helpful for learning.

aboobna · Answer

In these kind of questions when calculating percentage how to identify which value should we take should it be for red paint or blue paint? how do we understand that?

Bunuel · Answer

When calculating percentage change, the reference value is the value you are comparing  to . This means the reference value always goes in the  denominator  of the formula.

In this problem, the question asks: What percent less is the cost per square meter when using red paint  compared to  blue paint? Since we are comparing red to blue, the reference value is the blue paint’s cost, which is why the blue paint value goes in the denominator.

ZeroSquare · Answer

if the question only asked how much less is cost of red than cost of blue, then we would have simply found only the difference?

Bunuel · Answer

Yes. If the question asked only “how much less,” we would find the absolute difference in cost per square meter.

Here, red costs 100 cents per square meter and blue costs 125 cents per square meter, so the difference is 25 cents.

But the question asks “what percent less,” so we compare that difference with the blue cost:

25/125 = 20%.

M39-78

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