F.3 Mathematics
M.C. Revision Exercise – Ch.2 Percentage
Solutions
Multiple-choice Questions
13033001
A sum of $15 000 is invested at an interest rate of 8% p.a. for 2 years. Find the amount received if the interest is compounded yearly.
A. $2 400
B. $2 496
C. $17 400
D. $17 496
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Solution:
The answer is D.
The amount
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13033002
Miss Lee borrows $5 000 from a bank at an interest rate of 3.6% p.a. and the interest is compounded monthly. Find the amount that Miss Lee owed the bank after 3 years correct to the nearest ten dollars.
A. $5 540
B. $5 560
C. $5 570
D. $5 600
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Solution:
The answer is C.
Interest rate = 3.6% p.a.
Interest rate per month
Total number of months in 3 years = 12 ´ 3 = 36
If $5 000 is borrowed from the bank, then
the amount
, cor. to the nearest ten dollars
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13033003
A sum of money is deposited in a bank at an interest rate of 12% p.a. and the interest is compounded yearly. If the amount received after 7 years is $6 000 more than the principal, find the principal. (Give the answer correct to the nearest thousand dollars.)
A. $3 000
B. $4 000
C. $5 000
D. $6 000
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Solution:
The answer is C.
Let the principal be $P, then
The principal is $5 000.
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13033004
Fanny deposits two equal sums of money in a bank at an interest rate of 2% p.a. for
3 years. Simple interest and compound interest (calculated once a year) are used to calculate two sums of money respectively. If the compound interest received is $151 more than the simple interest, find the amount of each sum of money.
A. $115 000
B. $125 000
C. $135 000
D. $155 000
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Solution:
The answer is B.
Let the amount of each sum of money be $P, then
if simple interest is used for calculation,
the amount =
= 1.06P
If compound interest is used for calculation,
the amount =
= 1.061 208P
If the compound interest is $151 more than the simple interest, then
1.061 208P – 1.06P = 151
0.001 208P = 151
P = 125 000
Each sum of money is $125 000.
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13033005
The value of a diamond is $62 500. If its value increases steadily at a rate of 12% every 5 years, what will be its value after 20 years? (Give the answer correct to the nearest hundred dollars.)
A. $98 300
B. $110 100
C. $150 000
D. $602 900
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Solution:
The answer is A.
Total number of 5-year periods in 20 years = = 4
The value of the diamond after 20 years
= $62 500 ´ (1 + 12%)4
= , cor. to the nearest hundred dollars
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13033006
The number of crimes in a city is 56 000 this year. If the number of crimes increases steadily at a rate of 5% per year, find the increase in the number of crimes after
4 years. (Give the answer correct to the nearest hundred.)
A. 2 800
B. 11 200
C. 12 100
D. 68 100
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Solution:
The answer is C.
The number of crimes after 4 years
= 56 000 ´ (1 + 5%)4
= 68 068, cor. to the nearest one
Increase in the number of crimes
= 68 068 – 56 000
= , cor. to the nearest hundred
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13033007
A cup of 250 mL of water decreased by 5% in capacity every 12 hours. Find the capacity of this cup of water after 3 days, correct to the nearest mL.
A. 175 mL
B. 184 mL
C. 213 mL
D. 214 mL
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Solution:
The answer is B.
Total number of 12-hour periods in 3 days = 2 ´ 3 = 6
The capacity of the cup of water after 3 days
= 250 ´ (1 – 5%)6 mL
= , cor. to the nearest mL
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13033008
In the past 4 years, the depreciation rate of a notebook computer is 30% every year. If the present value of the notebook computer is $2 401, find its value 4 years ago.
A. $5 000
B. $6 000
C. $9 000
D. $10 000
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Solution:
The answer is D.
Let the value of the notebook computer 4 years ago be $P, then
The value of the notebook computer 4 years ago is $10 000.
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13033009
The tutorial fee of a university in 2008 is $40 000. If the tutorial fee increases steadily at a rate of 20% every year, what will be the tutorial fee of the university in 2012?
A. $64 000
B. $69 120
C. $72 000
D. $82 944
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Solution:
The answer is D.
2012 − 2008 = 4
The tutorial fee of the university in 2012
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13033010
The total number of visitors to a website increases steadily at a rate of 25% every quarter. If the total number of visitors to the website at the beginning of this year is
30 000, find the total number of visitors to the website at the end of next year correct to the nearest 1 000.
A. 45 000
B. 90 000
C. 179 000
D. 224 000
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Solution:
The answer is C.
Total number of quarters in 2 years = 4 ´ 2 = 8
Total number of visitors to the website at the end of the next year
= 30 000 ´ (1 + 25%)8
= , cor. to the nearest 1 000
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13033011
From 2005, the number of wild leopards decreased by 10% every year. If the number of wild leopards is 15 000 in 2005, find the number of wild leopards in 2008.
A. 9 500
B. 10 500
C. 10 935
D. 12 150
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Solution:
The answer is C.
2008 – 2005 = 3
The number of wild leopards in 2008
= 15 000 ´ (1 – 10%)3
=
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13033012
In 2006, the number of students of a school was 600. The number of students increased by 15% in 2007. But in 2008, the number of students decreased by 20%. Find the number of students of the school in 2008.
A. 408
B. 552
C. 621
D. 1 104
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Solution:
The answer is B.
The number of students of the school in 2008
= 600 ´ (1 + 15%) ´ (1 – 20%)
= 600(1.15)(0.8)
=
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13033013
The area of a strawberry yard is 5 hectares. After the first harvest, the harvestable area decreased by 30% and after the second harvest, the remaining harvestable area decreased by 24%. Find the remaining harvestable area of the yard.
A. 1.96 hectares
B. 2.34 hectares
C. 2.66 hectares
D. 3.04 hectares
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Solution:
The answer is C.
The remaining harvestable area of the strawberry yard
= 5 ´ (1 – 30%) ´ (1 – 24%) hectares
= 5(0.7)(0.76) hectares
=
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13033014
Suppose d = vt, if the value of v decreased by 14% and the value of t increased by 6%, find the percentage change in the value of d, correct to the nearest 1%.
A. –9%
B. –7%
C. +7%
D. +9%
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Solution:
The answer is A.
New value of d = v(1 – 14%)t(1 + 6%)
= (0.86)(1.06)vt
= 0.911 6vt
The percentage change in the value of d
= , cor. to the nearest 1%
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13033015
Which of the following result is greater than the original value?
A. A number is first decreased by 10%, and then increased by 9%.
B. A number is first decreased by 10%, and then increased by 11%.
C. A number is first decreased by 9%, and then increased by 9%.
D. A number is first decreased by 9%, and then increased by 10%.
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Solution:
The answer is D.
Let the number be x.
A: (1 – 10%)(1 + 9%)x = (0.9)(1.09)x = 0.981x
B: (1 – 10%)(1+ 11%)x = (0.9)(1.11)x = 0.999x
C: (1 – 9%)(1 + 9%)x = (0.91)(1.09)x = 0.991 9x
D: (1 – 9%)(1 + 10%)x = (0.91)(1.1)x = 1.001x
The answer is D.
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13033016
Last year, the price of a stock was increased by 90%. But this year, the price is decreased by 45%. Find the percentage change in the price of this stock.
A. –30.5%
B. –4.5%
C. +4.5%
D. +30.5%
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Solution:
The answer is C.
Let the price of the stock before last year be $P, then
the price this year
= $P(1 + 90%)(1 – 45%)
= $P(1.9)(0.55)
= $1.045P
The percentage change in the price of the stock
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13033017
The costs of employing workers and buying materials for the renovation of a flat are $20 000 and $15 000 respectively. If the cost of employing the workers is increased by 10% and that for buying the materials is decreased by 25%, what is the percentage change in the cost for renovating this flat?
A. –15%
B. –5%
C. +5%
D. +15%
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Solution:
The answer is B.
Original total cost = $(20 000 + 15 000)
= $35 000
New cost of employing workers = $20 000 ´ (1 + 10%)
= $22 000
New cost of buying materials = $15 000 ´ (1 – 25%)
= $11 250
New total cost = $(22 000 + 11 250)
= $33 250
The percentage change in the total cost
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13033018
A number is first decreased by 20% and then increased by 20%. Find the percentage change in the value of the number.
A. –20%
B. –4%
C. +4%
D. remain unchanged
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Solution:
The answer is B.
Let the number be x.
The new value of the number = x(1 – 20%)(1 + 20%)
= x(0.8)(1.2)
= 0.96x
The percentage change in the value of the number
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13033019
A number is first increased by 10% and then decreased by 30%, the result is 770. Find the number.
A. 700
B. 800
C. 1 000
D. 1 100
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Solution:
The answer is C.
Let the number be x, then
x(1 + 10%)(1 – 30%) = 770
0.77x = 770
x = 1 000
The number is 1 000.
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13033020
The area of a square picture is 144% of the original area after enlargement. What is the percentage increase in the length of its sides after enlargement?
A. 44%
B. 20%
C. 12%
D. 4%
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Solution:
The answer is B.
Let the original length of the square be x, then
new area = 1.44x2
Let the length of the square after enlargement be y, then
The percentage increase in the length of the square
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13033021
The daily working hours of William is increased from 8 hours to 10 hours. But his hourly wage is decreased by 15%. Find the percentage change in William’s daily income.
A. an increase of 6.67%
B. an increase of 6.25%
C. a decrease of 6.25%
D. remain unchanged
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Solution:
The answer is B.
Let the original hourly wage of William be $H, then
original daily income = $8H
new daily income = $H ´ 10 ´ (1 – 15%) = $8.5H
The percentage change in William’s daily income
William’s daily income has an increase of 6.25%.
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13033022
As the charge of each unit of electricity is increased by 15%, a hotel reduces its electricity consumption by 20%. Find the percentage change in the expenditure on electricity.
A. +8%
B. +2%
C. –2%
D. –8%
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Solution:
The answer is D.
Let the original charge of each unit of electricity be $x and the original electricity consumption be y units.
Original electricity charge = $xy
New charge of each unit of electricity = $x ´ (1 + 15%)
= $1.15x
New electricity consumption = y ´ (1 – 20%) units
= 0.8y units
New electricity charge = $(1.15x)(0.8y)
= $0.92xy
The percentage change in expenditure on electricity
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13033023
The price of a portable game player after it first released was $1 500. If the price of the game player increased by 20% every 2 months for the first 6 months but then its price decreased by 10% every month, find the price of the portable game player
9 months after it released to the market, correct to the nearest dollar.
A. $1 004
B. $1 022
C. $1 890
D. $3 265
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Solution:
The answer is C.
Total number of 2-month periods in 6 months = = 3
The price of the portable game player 9 months after it released
= $1 500 ´ (1 + 20%)3 ´ (1 – 10%)3
= , cor. to the nearest dollar
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13033024
The value of a second-hand motor bike was $12 000. From June, its value decreased by 30% per month, but its value increased by 20% per month from August. Find the value of the motor bike in August.