# EXPRESSING ONE QUANTITY AS A PERCENTAGE OF ANOTHER

To express one quantity as a percentage of another, we have to follow the procedure given below.

Step 1 :

Express the given quantities as fraction.

Step 2 :

If we want to convert the  decimal or fraction as percentage, we have to multiply it by 100%.

Write the first quantity as percentage of the second.

Problem 1 :

36 out of 72

Solution :

Step 1 :

Expressing as fraction :

= 36/72

Step 2 :

= (36/72) x 100%

= (1/2) x 100%

= 50%

Problem 2 :

77 out of 440

Solution :

Step 1 :

Expressing as fraction :

= 77/440

Step 2 :

= (77/440) x 100%

Problem 3 :

180 out of 900

Solution :

= 180 out of 900

Expressing as fraction,

= (180 / 900)

Converting into percentage :

= (180 / 900) x 100%

= 20%

Problem 4 :

A school football team plays 25 games in a season. They win 17, draw 2 and lose the rest. Express the numbers won, draw and lost as percentage of the total number of games played.

Solution :

Total number of games played = 25

Number of games they won = 17

Number of games they met draw = 2

Number of games they lost = 25 - (17 + 2)

= 25 - 19

= 6

Percentage of games they won :

= (17/25) x 100%

= 68%

Percentage of games they met draw :

= (2/25) x 100%

= 8%

Percentage of games they lost :

= (6/25) x 100%

= 24%

Other way to find percentage of people they lost :

= 100% - (68% + 8%)

= 100% - 76%

= 24%

Problem 5 :

An airline has a fleet of 80 planes. Of these, 10 are being serviced at any one time. What percentage of the fleet is available for flights ?

Solution :

Total number of planes = 80

Planes which are being serviced = 80 - 10

= 70

Percentage of planes available for flights = (70/80) x 100%

= (7/8) x 100%

= 87.5%

Problem 6 :

A car manufacturer produces 175000 sports cars a year. They are only available in white, black and red. 52500 are white, 78750 are black and the rest are red.

a)  What percentage of the cars are black ?

b) What percentage are white ?

c) What percentage are red ?

Solution :

Number of cars produces = 175000

Number of cars available in white = 52500

Number of cars available in black = 78750

Number of available in red = 175000 - (52500 + 78750)

= 175000 - 131250

= 43750

a) percentage of the cars that are black :

= (78750/175000) x 100%

= 0.45 x 100%

= 45%

b) percentage of cars that are white :

= (52500/175000) x 100%

= 0.3 x 100%

= 30%

c) percentage of cars that are red :

= (43750/175000) x 100%

= 0.25 x 100%

= 25%

Problem 7 :

Sylvia answered 62% of the students on a math test correctly.

They were 30 questions on the test.

How many questions did Sylvia answer correctly ?

Solution :

Number of question on the test = 30

Percentage of students who answered correctly = 62%

Number of students who answered correctly = 62% of 30

= 0.62(30)

= 18.6

Number of questions she has answered correctly is 19.

Problem 8 :

In a class of 28, 16 pupils are girls. What percentage of the class are boys ?

Solution :

Total number of students in the class = 28

Number of girls = 16

Number of boys + number of girls = 28

Number of boys = 28 - 16

= 14

Percentage of boys = (14/28) x 100%

= (1/2) x 100%

= 50%

So, the percentage of boys is 50%.

Problem 9 :

A car journey took 7 hours to complete. What percentage of the day was spent on the journey ?

Solution :

Total number of hours in a day = 24

Number of hours taking for journey = 7

Percentage of hours took for journey = (7/24) x 100%

= (0.291) x 100%

= 29.1

Approximately 29%.

Problem 10 :

The number of trees in the forest increased from 80 to 125 from 2001 to 2006. What percentage had the number of trees increased ?

Solution :

Number of trees on 2001 = 80

Number of trees on 2006 = 125

Number of trees increasing = 125 - 80

= 45

Percentage of trees increasing = (45/80) x 100%

= (0.5625) x 100%

= 56.25 %

So, the percentage of increase is approximately 56%.

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