CALCULATING PERCENTAGES
To calculate the percentage of any amount change the question into a
multiplication problem.
Example 1. What is 25% of 3000?
Solution
25%of
3000= 25 × 3000
100
25% of 3000=
750.
Example 2. John bought a pair of
slippers for 2000F C FA. He was given a
discount of 20%. How much did he pay for the slippers?
Solution
Discount is
20% of 2000F= 20 × 2000F
100
Discount of
20%= 400F C FA.
Amount paid
for the slippers= 2000F- 400F
Amount paid
for the slippers= 1600F.
Example 3. Mary bought a computer game
that was to be sold for 64000F
CFA at a discount of 30%. How much did she pay for the game?
CFA at a discount of 30%. How much did she pay for the game?
Solution
Discount is 30% of 64000F= 30 ×64000F
100
Discount is
30% of 64000F= 19200F
Amount paid
for the game= 64000F- 19200F
Amount paid
for the game=44800F.
Example 4. In a college of 800
students, 500 are girls.
a)
What percentage of the students are girls?
b)
What is the percentage of boys in the college?
Solution
Total
number of students=800
Number
of girls= 500
Number
of boys=800-500
Number
of boys=300.
a.
Percentage of girls= 500 ×100
800
Percentage
of girls=.625×100
Percentage
of girls= 62.5%
b.
Percentage of boys=300 ×100
800
Percentage
of boys=.375×100
Percentage
of boys=37.5%
Example 5. A high school has 4000
students. During an assembly, only 3750 students were present.
a)
What percentage of the students was present
b)
What percentage of the students was absent?
Solution
Total number of students in the school= 4000
Number present=3750
Number absent=4000-3750
Number absent=250
a)
Percentage of students present= 3750 ×100
4000
Percentage
of students present= 0.9375×100
Percentage
of students present= 93.75%
b)
Percentage of students absent= 250×100
4000
Percentage
of students absent= .0625×100
Percentage
of students absent=6.25%
Example 6. Dominic earns 250,000 FRS CFA.
Every month, he divides his salary as follows:
100,000 FRS
for savings
75,000FRS
for food
25,000FRS
for health care.
a)
How much of his salary is left all these
expenses?
b)
What percentage of the salary is left after all
expenses is deducted?
c)
What percentage of his salary does he save?
Solution
Total salary= 250,000FRS
Total spent on savings, food, and health care=
100,000+75,000+25,000
Hence total spent on savings, food, and health
care= 200,000FRS
a)
Money left after all the expenses=
250,000FRS-200,000FRS
Money left after all expenses=50,000FRS.
b)
Percentage of salary left after all expenses= 50,000
×100 =20%
250,000
c)
Percentage of salary saved= 100,000×100 =
40%
250,000
Example 7. In a class of 36 students,
75% passed the promotion examination.
a)
How many students passed the examination?
b)
How many of them failed the promotion
examination?
Solution
a)
Total number in class=36
Let number that passed= P
Percentage pass=75%
Number passed× 100=Percentage pass
Total in class
P
×100 = 75
36
P= 75×36 = 27
100
P= 27, hence 27 students passed the promotion
examination.
b)
Number that failed= total in class- number that
passed
Number
that failed= 36-27
Number
that failed= 9.
Another Method.
If
75% passed, it means 25% failed.
Let
the number that failed be F
Percentage
failed=25%
Number
failed ×100 = percentage failed
Total
in class
F× 100=25
36
F = 25×36 = 9
100
F=
9, hence 9 students failed the promotion examination.
CALCULATING PROFIT OR LOSS IN TERMS OF PERCENTAGES.
When we buy
or sell something we usually make a profit or a loss. When we sell the item for
more than we paid for, we make a profit. If we sell it less money than we paid
for it, we make a loss. Businesses usually calculate their profit or loss as a
percentage of the price they paid for the goods. The price the business pays
for the goods is the cost price (CP) and the price goods are sold is called
selling price (SP).
EXAMPLE 1.
Joan bought a pair of shoes for 25000FRS and later sold it for
30,000FRS.Calculate:
a)
The amount made as profit
b)
The percentage profit.
Solution
a)
Cost price (CP)=25000FRS
Selling
price (SP)= 30,000FRS
Profit=
selling price-cost price
Profit=
30,000FRS-25,000FRS
Profit=5000FRS.
b)
To find the percentage profit that she made,
write the fraction profit
Cost price
And convert
this fraction to a percentage.
Percentage profit= 5,000 × 100
25000 1
Percentage profit = 20%
EXAMPLE 2. Elvis bought a bicycle for
80,000FRS and later sold it for 50,000FRS because it had a no brakes. Calculate:
a)
The amount lost
b)
The percentage loss
Solution
a)
Cost price= 80,000FRS
Selling
price= 50,000FRS
Loss=
cost price- selling price
Loss=
80,000FRS- 50,000FRS
Loss=
30,000FRS.
b)
Percentage loss= 30,000 ×100
80,000 1
Percentage
Loss= 37.5%
EXAMPLE 3. In order to attract
passengers, a travel agency decides to reduce transport from 4000F C FA to
2500FCFA from Bamenda to Mamfe. What is the percentage loss this agency
incurred?
Solution
Cost price=
4000F C FA
Selling
price= 2500F C FA
Amount lost=
4000F- 2500F
Amount
lost=1500F
Percentage
loss= 1500F×100
4000F
Percentage
loss= 37.5%
EXAMPLE 4. The price of kerosene
increased by 20%. If the initial cost was 200FCFA per can, what was the new
price?
Solution.
Using
percentages.
Initial
price of 200FCFA is equivalent to 100%
New price X
is equivalent to (100+20)%= 120%
Using
proportions; X: 200FCFA= 100%: 120%
X =
120%
200FCFA 100%
X = 120
×200F C FA
100
X=240FCFA
Hence new
price is 240FCFA.
EXERCISE
1)
A business man is in financial difficulty and
decides to sell his car that cost him 2, 000,000FCFA for 1,750,000FCFA. What is
the percentage decrease in the price of the car?
2)
Mr. Paul
bought a mobile telephone that was to be sold for 45,000FCFA at a discount of
30%. How much did he pay?
3)
In a class of 58 students, 62% passed the
promotion examination.
a)
How many students passed the promotion
examination?
b)
How many of them failed the promotion
examination?
c)
What percentage failed the promotion
examination?
4)
In mathematics with the maximum mark of 100,
Peter scored 56 marks.
a)
What percent of the total mark did he have?
b)
What percentage of the total mark did he miss?
5)
In an election involving three political parties
A,B and C, 15% voted for party A, 23% voted for party B and 20% boycotted the
election. What percentage voted for party C.
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