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%.
May 21, 24 08:51 PM
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