Percent Math Questions




Several questions on percentages, with detailed solutions are presented.

Question 1:

What percentage of the large square is colored red in each figure below?

percent 1 a
percent 1 b
percent 1 a
percent 1 b

Solution to Question 1

  • In figure A, 1 small square out of a total of 100 is colored red, the answer is

    1 / 100 = 1%

  • In figure B, 41 small squares out of a total of 100 are colored red, the answer is

    41 / 100 = 41%

  • In figure C, 50 small squares out of a total of 100 are colored red, the answer is

    50 / 100 = 50% which is also equal to one half.

  • In figure D, 100 small squares out of a total of 100 are colored red, the answer is

    100 / 100 = 100% which is also equal to one.


Question 2:

What percent of the balls in the figure below are red?

percent 2

Solution to Question 2

  • 5 balls out of a total of nine are red, so in fraction we have

    5 / 9

  • divide 5 by 9 to obtain

    5 / 9 = 0.56 (rounded to 2 decimal places)

  • Multiply and divide 0.56 by 100 to obtain

    = 0.56 * 100 / 100 = 56 / 100 = 56%

  • Approximately 56% of the balls in the above figure are red.


Question 3:

What is 12% of 250?

Solution to Question 3

  • "what" in the above question is the unknown; we denote by y. The word "of" represents a multiplication and "is" represents equal. The above question may be translated in mathematical form as follows

    y = 12% * 250

  • Rewrite the percentage ( 12% ) as a fraction in the above equation

    y = [ 12 / 100 ] * 250 = [12 * 250 ] / 100 = 30

  • 12% of 250 is equal to 30.


Question 4:

4 is what percent of 32?

Solution to Question 4

  • Let the unknown "what percent" be denoted by y%, since we are looking for a percentage. "is" is represented by equal and "of" by a multiplication. Hence the above question may be translated into a math equation as follows:

    4 = y% * 32

  • We now solve for the unknown y%

    y% = 4 / 32 = 0.125

  • We have found the decimal form to y% which can be changed into percentage form by multiplying and dividing it by 100. Hence

    y% = 0.125 = 12.5 / 100 = 12.5%

  • As an exercise, check that 12.5% of 32 gives 4.


Question 5:

6 is 80% of what number?

Solution to Question 5

  • Let x be the unknown, "what number" in the above question. The word "of" represents a multiplication and "is" represent =. Hence the above question may be translated into a math equation as follows:

    6 = 80% * x

  • Solve for x to obtain

    x = 6 / 80%

  • Rewrite the percentage 80% as a fraction in the above equation.

    x = 6 / [80 / 100]

  • To divide 6 by the fraction 80/100 multiply by the reciprocal of the fraction 80/100. Hence.

    x = 6 * [100 / 80] = 600 / 80 = 7.5

  • As an exercise, check that 80% of 7.5 gives 6.


Question 6:

A number increased from 120 to 150. By what percent, of its original value, did this number increase?

Solution to Question 6

  • A percent represent a part of a whole or a fraction with the denominator equal to 100. The part here is the absolute increase given by

    part = 150 - 120 = 30

  • The whole is the original value, 120, hence the unknown percent x is given by

    x = part / whole = 30 / 120 = 0.25

  • Multiply 0.25 by 100 and divide it by 100 to obtain.

    x = 0.25 * 100 / 100 = 25 / 100 = 25%

  • An increase from 120 to 150 is equivalent to a 25% increase of the original value 120.


Question 7:

A number decreased from 80 to 50. By what percent of its original value has this number decreased?

Solution to Question 7

  • The part here is given by

    part = 80 - 50 = 30

  • The whole is the original value, 80, hence the percent x is given by

    x = part / whole = 30 / 80 = 0.375

  • Multiply 0.375 by 100 and divide it by 100 to convert it into percentage.

    x = 0.375* 100 / 100 = 37.5 / 100 = 37.5%

  • A decrease from 80 to 50 is equivalent to a 37.5% decrease of the original value 80.


Question 8:

Which is greater 15% of 380 or 25 of 210?

Solution to Question 8

  • Let x = 15% of 380, hence

    x = 15% * 380 = (15 / 100) * 80 = 15 * 380/100 = 57

  • Let y = 25% of 210, hence

    y = 25% * 210 = (25/100) * 210 = 52.5

  • 15% of 380 is greater than 25 of 210



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Updated: 2 April 2013

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