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Grade 6Percentage
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Answer the questions
(1) The chart shows production of dif f erent f ruits in a f arm. If production of apple was 4875 Kg,f ind the production of grapes.
(2) Mark's income is 30% less than Jennif er's income, Brian's income is 30% less than Mark'sincome, and Sandra's income is 20% less than Mark's income. If Jennif er gave 70% of hisincome to Brian and 30% of his income to Sandra. What would be the f raction of Brian's newincome and Sandra's new income?
(3) Convert the f raction representation of a percentage into the decimal f orm:
A) 49
7
10 %
B) 48
13
20 %
C) 79
4
5 %
D) 90
13
20 %
E) 38
2
5 %
F) 4
1
2 %
(4) When 9 is added to 90 % of a number, it gives the number itself . f ind the number.
(5) 3.2 is what percent of 8000?
(6) Anthony donated 20% of his salary to charity and spent 20% of the remaining amount. He stillhas $4800 lef t. What was his total salary?
Choose correct answer(s) from given choice
(7) One ticket to a show costs $ 20. Nancy buys a total of 5 t ickets f or the show using a couponthat gives her a 15% discount. Lisa buys 10 tickets using a coupon that gives a 20% discount.How much more did Lisa pay than Nancy?
a. $ 75 b. $ 79
c. $ 72 d. $ 73
(8) (13% of 55) - (55% of 13) =
a. -2 b. 0
c. 2 d. 1
ID : ww-6-Percentage [1]
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(9) Solve the f ollowing:
20 % of 977 is:
a. 197.38 b. 205.05
c. 195.4 d. 187.84
(10) A bear is walking on periphery of a regular polygon as shown below.
If it starts f rom point s, bear will be on which side af ter walking 92% distance of the periphery inclock-wise direction?
a. D b. A
c. E d. B
Fill in the blanks
(11) Convert the f ollowing ratios into percent:
A)21:50 = %
B)132:400 = %
C)7:100 = %
D)31:100 = %
E)1:10 = %
F)3:10 = %
(12) Find the number whose:
A)0.42 is 42% of number ?
B)3.84 is 32% of number ?
C)1.12 is 16% of number ?
D)1.11 is 37% of number ?
(13) Find:
A) 1% of Rs. 692 =
Rs.
B) 4% of 553 hours =
hours
C) 50% of 507 seconds =
seconds
D) 30% of Rs. 459 =
Rs.
E) 50% of 195 meters =
meters
F) 0.2% of 757 seconds =
seconds
(14) Fill the number which satisf ies the condition :
ID : ww-6-Percentage [2]
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A) 16
4 % of = 4.16
B) 18
72 % of = 1.26
C) 54
48 % of = 16.74
D) 6
9 % of = 0.18
Check True/False
(15) 26% of 47% of 1200 = 47% of 26% of 1200 True False
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Answers
(1) 14625 Kg
Step 1
If you look at the given chart caref ully, you will notice that the production of f ruits guava,apple, grapes, peach in a f arm is 25%, 12.5%, 37.5%, 25% respectively.
Step 2
Since production of apple is 4875 Kg, which is 12.5% of a f arm.or we can say that the 12.5% production of a f arm = 4875 Kg
⇒ 1% production of a f arm = 4875
12.5
⇒ 37.5% production of a f arm = 4875
12.5 × 37.5 = 14625 Kg
Step 3
Since production of grapes is 37.5% of a f orm and 37.5% production of a f arm is 14625Kg,theref ore the production of grapes will be 14625 Kg.
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(2) 119
86
Step 1
In the question, there are f our people: Mark, Brian, Sandra and Jennif er. Everyone's incomeis directly or indirectly told in terms of Jennif er's income.
Step 2
Let's write Mark's, Brian's and Sandra's income as a percentage of Jennif er's income f irst.
Step 3
Mark's income:Mark's income is 30% less than Mark's income. This means,Mark's income is (100 - 30) = 70% of Jennifer's income
Step 4
Brian's income:Brian's income is 30% less than Mark's income. This means,Brian's income is (100 - 30) = 70% of Mark's income= 70% of 70% of Jennif er's income ...[Mark's income is 70% of Jennifer's income]= 70% × 70% of Jennif er's income= (70 × 70)/100 % of Jennif er's income ...[When we multiply two percentages, we needto divide by 100 to get f inal percentage]= 4900/100 % of Jennif er's income= 49% of Jennif er's income
Step 5
Sandra's income:Sandra's income is 20% less than Mark's income. This means,Sandra's income is (100 - 20) = 80% of Mark's income= 80% of 70% of Jennif er's income= 80% × 70% of Jennif er's income= (80 × 70)/100 % of Jennif er's income= 56% of Jennif er's income
Step 6
We have just f ound that:Brian's income = 49% of Jennifer's incomeSandra's income = 56% of Jennifer's income
Jennif er gives 70% of his income to Brian and 30% of his income to Sandra. Their newincomes will be:
Brian's new income = (49 + 70) = 119% of Jennifer's incomeSandra's new income = (56 + 30) = 86% of Jennifer's income
Step 7
Fraction of Brian's new income to Sandra's new income = (119% of Jennif er'sincome)/(86% of Jennif er's income)
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= 119
86
(3) A) 0.497
Step 1
First of all we have to change the mixed f raction representation of the
percentage 497
10 % into the f raction representation of the percentage, by
multiplying the denominator 10 to the whole number 49 and add the result to thenumerator 7, as below:
497
10 % =
497
10 %
Step 2
Now, convert the f raction represent of the percentage 497
10 % into the simple
f raction, dividing by 100:
497
10 %
= 497
10 × 100
= 497
1000
= 0.497
Step 3
Hence, the f raction representation of the percentage into the decimal f orm is0.497 .
ID : ww-6-Percentage [6]
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B) 0.4865
Step 1
First of all we have to change the mixed f raction representation of the
percentage 4813
20 % into the f raction representation of the percentage, by
multiplying the denominator 20 to the whole number 48 and add the result to thenumerator 13, as below:
4813
20 % =
973
20 %
Step 2
Now, convert the f raction represent of the percentage 973
20 % into the simple
f raction, dividing by 100:
973
20 %
= 973
20 × 100
= 973
2000
= 0.4865
Step 3
Hence, the f raction representation of the percentage into the decimal f orm is0.4865.
ID : ww-6-Percentage [7]
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C) 0.798
Step 1
First of all we have to change the mixed f raction representation of the
percentage 794
5 % into the f raction representation of the percentage, by
multiplying the denominator 5 to the whole number 79 and add the result to thenumerator 4, as below:
794
5 % =
399
5 %
Step 2
Now, convert the f raction represent of the percentage 399
5 % into the simple
f raction, dividing by 100:
399
5 %
= 399
5 × 100
= 399
500
= 0.798
Step 3
Hence, the f raction representation of the percentage into the decimal f orm is0.798.
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D) 0.9065
Step 1
First of all we have to change the mixed f raction representation of the
percentage 9013
20 % into the f raction representation of the percentage, by
multiplying the denominator 20 to the whole number 90 and add the result to thenumerator 13, as below:
9013
20 % =
1813
20 %
Step 2
Now, convert the f raction represent of the percentage 1813
20 % into the simple
f raction, dividing by 100:
1813
20 %
= 1813
20 × 100
= 1813
2000
= 0.9065
Step 3
Hence, the f raction representation of the percentage into the decimal f orm is0.9065.
ID : ww-6-Percentage [9]
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E) 0.384
Step 1
First of all we have to change the mixed f raction representation of the
percentage 382
5 % into the f raction representation of the percentage, by
multiplying the denominator 5 to the whole number 38 and add the result to thenumerator 2, as below:
382
5 % =
192
5 %
Step 2
Now, convert the f raction represent of the percentage 192
5 % into the simple
f raction, dividing by 100:
192
5 %
= 192
5 × 100
= 192
500
= 0.384
Step 3
Hence, the f raction representation of the percentage into the decimal f orm is0.384 .
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F) 0.045
Step 1
First of all we have to change the mixed f raction representation of the
percentage 41
2 % into the f raction representation of the percentage, by
multiplying the denominator 2 to the whole number 4 and add the result to thenumerator 1, as below:
41
2 % =
9
2 %
Step 2
Now, convert the f raction represent of the percentage 9
2 % into the simple
f raction, dividing by 100:
9
2 %
= 9
2 × 100
= 9
200
= 0.045
Step 3
Hence, the f raction representation of the percentage into the decimal f orm is0.045.
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(4) 90
Step 1
Lets assume that the number is x,
90 % of x = x × 90
100 =
90x
100
Step 2
If you look at the question caref ully, you will notice that the number(x) is equal to the sumof 9 and 90 % of x,It can be written as:
x = 9 + 90x
100
⇒ x = 9 × 100 + 90x
100
⇒ x = 900 + 90x
100
By cross multiplying both sides100x = 900 + 90x⇒ 100x - 90x = 900⇒ 10x = 900
⇒ x = 900
10
⇒ x = 90
Step 3
Theref ore the number is 90.
(5) 0.04%
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(6) $7500
Step 1
Let's assume the total salary of the man be x
Step 2
Af ter donating 20%, percentage amount lef t with him = 100 - 20% = 80%.Theref ore amount remaining af ter donation = (80x / 100)
Step 3
Similarly percentage amount remaing with him af ter spending 20% = 100 - 20% = 80%Theref ore amount remaining af ter spending = (80 (80x / 100) / 100),
= (80)(80)x
10000
Step 4
Since remaining amount is given in question to be $4800,
(80)(80)x
10000 = 4800
⇒ x = (4800)(10000)
(80)(80)
⇒ x = 7500
Step 5
Theref ore, his total salary was $7500.
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(7) a. $ 75
Step 1
Nancy buys 5 tickets f or the show using a coupon that gives her a 15% discount.The price of 5 t ickets = 5 × 20 = $100The amount paid by Nancy f or 5 t ickets = The price of 5 t ickets - 15% discount
= 100 - 100 × 15
100
= 100 - 1500
100
= 100 - 15= $85
Step 2
Lisa buys 10 tickets f or the show using a coupon that gives her a 20% discount.The price of 10 tickets = 10 × 20 = $200The amount paid by Lisa f or 10 tickets = The price of 10 tickets - 20% discount
= 200 - 200 × 20
100
= 200 - 4000
100
= 200 - 40= $160
Step 3
Theref ore the amount that Lisa pays more than Nancy,= 160 - 85= $75
(8) b. 0
Step 1
(13% of 55) = 55 × 13/100⇒ (13% of 55) = (13 × 55)/100
Step 2
(55% of 13) = 13 × 55/100⇒ (55% of 13) = (13 × 55)/100
Step 3
Now we can f ind value of required expression,(13% of 55) - (55% of 13)= (13 × 55)/100 - (13 × 55)/100,= 0
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(9) c. 195.4
Step 1
We have been asked to f ind the value of 20 % of 977.
Step 2
20 % of 977 means = 977 × 20 %
= 977 × 20
100
= 19540
100
= 195.4
Step 3
Theref ore, 20 % of 977 is 195.4.
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(10) c. E
Step 1
If you look at the regular polygon caref ully, you will notice that the number of sides of aregular polygon are 5.
Theref ore the length of a side of the regular polygon = 1
5
Step 2
Since distance walked by a bear on the periphery in clock-wise direction = 92% = 92
100
Theref ore the number of sides walked by a bear on the regular polygon =
Distance walked by a bear
Length of a side of the polygon
=
92
100
1
5
= 92
100 ×
5
1
= 460
100
= 4.6
It means bear walked on 4 sides of the regular polygon and a bear is walking on the 5th sideof the regular polygon in clock-wise direction.
Step 3
Since it starts f rom point s, bear will be on the side E af ter walking 92 distance of theperiphery in clock-wise direction.
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(11) A) 42
Step 1
To convert ratio 21:50 into percent, f irst of all convert ratio 21:50 into f ractionand multiplying it by 100 and adding percentage symbol(%).Theref ore ratio 21:50 can be written as:
21:50 = 21
50 × 100 %
= 2100
50
= 42 %
Step 2
Theref ore the percent of ratio 21:50 is 42 %.
B) 33
Step 1
To convert ratio 132:400 into percent, f irst of all convert ratio 132:400 intof raction and multiplying it by 100 and adding percentage symbol(%).Theref ore ratio 132:400 can be written as:
132:400 = 132
400 × 100 %
= 13200
400
= 33 %
Step 2
Theref ore the percent of ratio 132:400 is 33 %.
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C) 7
Step 1
To convert ratio 7:100 into percent, f irst of all convert ratio 7:100 into f ractionand multiplying it by 100 and adding percentage symbol(%).Theref ore ratio 7:100 can be written as:
7:100 = 7
100 × 100 %
= 700
100
= 7 %
Step 2
Theref ore the percent of ratio 7:100 is 7 %.
D) 31
Step 1
To convert ratio 31:100 into percent, f irst of all convert ratio 31:100 into f ractionand multiplying it by 100 and adding percentage symbol(%).Theref ore ratio 31:100 can be written as:
31:100 = 31
100 × 100 %
= 3100
100
= 31 %
Step 2
Theref ore the percent of ratio 31:100 is 31 %.
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E) 10
Step 1
To convert ratio 1:10 into percent, f irst of all convert ratio 1:10 into f raction andmultiplying it by 100 and adding percentage symbol(%).Theref ore ratio 1:10 can be written as:
1:10 = 1
10 × 100 %
= 100
10
= 10 %
Step 2
Theref ore the percent of ratio 1:10 is 10 %.
F) 30
Step 1
To convert ratio 3:10 into percent, f irst of all convert ratio 3:10 into f raction andmultiplying it by 100 and adding percentage symbol(%).Theref ore ratio 3:10 can be written as:
3:10 = 3
10 × 100 %
= 300
10
= 30 %
Step 2
Theref ore the percent of ratio 3:10 is 30 %.
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(12) A) 1
Step 1
Lets assume 0.42 is 42% of x.
Step 2
Now we can represents 0.42 is 42% of x as:x × 42% = 0.42
⇒ x × 42
100 = 0.42
⇒ x = 0.42 × 100
42
⇒ x = 42
42
⇒ x = 1
Step 3
Theref ore we can say that 0.42 is 42% of 1.
B) 12
Step 1
Lets assume 3.84 is 32% of x.
Step 2
Now we can represents 3.84 is 32% of x as:x × 32% = 3.84
⇒ x × 32
100 = 3.84
⇒ x = 3.84 × 100
32
⇒ x = 384
32
⇒ x = 12
Step 3
Theref ore we can say that 3.84 is 32% of 12.
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C) 7
Step 1
Lets assume 1.12 is 16% of x.
Step 2
Now we can represents 1.12 is 16% of x as:x × 16% = 1.12
⇒ x × 16
100 = 1.12
⇒ x = 1.12 × 100
16
⇒ x = 112
16
⇒ x = 7
Step 3
Theref ore we can say that 1.12 is 16% of 7 .
D) 3
Step 1
Lets assume 1.11 is 37% of x.
Step 2
Now we can represents 1.11 is 37% of x as:x × 37% = 1.11
⇒ x × 37
100 = 1.11
⇒ x = 1.11 × 100
37
⇒ x = 111
37
⇒ x = 3
Step 3
Theref ore we can say that 1.11 is 37% of 3.
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(13) A) 6.92
Step 1
If you read the question caref ully, you will notice that you have to f ind out the1% of Rs. 692.
Step 2
We can write 1% of Rs. 692 as:1% of Rs. 692 = 692 × 1%
= 692 × 1
100
= 692
100
= 6.92 Rs.
Step 3
Now 1% of Rs. 692 is 6.92 Rs..
B) 22.12
Step 1
If you read the question caref ully, you will notice that you have to f ind out the4% of 553 hours.
Step 2
We can write 4% of 553 hours as:4% of 553 hours = 553 × 4%
= 553 × 4
100
= 2212
100
= 22.12 hours
Step 3
Now 4% of 553 hours is 22.12 hours.
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C) 253.5
Step 1
If you read the question caref ully, you will notice that you have to f ind out the50% of 507 seconds.
Step 2
We can write 50% of 507 seconds as:50% of 507 seconds = 507 × 50%
= 507 × 50
100
= 25350
100
= 253.5 seconds
Step 3
Now 50% of 507 seconds is 253.5 seconds.
D) 137.7
Step 1
If you read the question caref ully, you will notice that you have to f ind out the30% of Rs. 459.
Step 2
We can write 30% of Rs. 459 as:30% of Rs. 459 = 459 × 30%
= 459 × 30
100
= 13770
100
= 137.7 Rs.
Step 3
Now 30% of Rs. 459 is 137.7 Rs..
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E) 97.5
Step 1
If you read the question caref ully, you will notice that you have to f ind out the50% of 195 meters.
Step 2
We can write 50% of 195 meters as:50% of 195 meters = 195 × 50%
= 195 × 50
100
= 9750
100
= 97.5 meters
Step 3
Now 50% of 195 meters is 97.5 meters.
F) 1.514
Step 1
If you read the question caref ully, you will notice that you have to f ind out the0.2% of 757 seconds.
Step 2
We can write 0.2% of 757 seconds as:0.2% of 757 seconds = 757 × 0.2%
= 757 × 0.2
100
= 151.4
100
= 1.514 seconds
Step 3
Now 0.2% of 757 seconds is 1.514 seconds.
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(14) A) 104
Step 1
Lets assume x is the number whose 16
4 % is 4.16.
Step 2
Now we can represents 16
4 % of x is 4.16 as:
x × 16
4 % = 4.16
⇒ x × 16
4 × 100 = 4.16
⇒ x × 1600
4 = 4.16
⇒ x = 4.16 × 4
1600
⇒ x = 104
Step 3
Theref ore we can say that the number whose 16
4 % is 4.16, is 104.
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B) 504
Step 1
Lets assume x is the number whose 18
72 % is 1.26.
Step 2
Now we can represents 18
72 % of x is 1.26 as:
x × 18
72 % = 1.26
⇒ x × 18
72 × 100 = 1.26
⇒ x × 1800
72 = 1.26
⇒ x = 1.26 × 72
1800
⇒ x = 504
Step 3
Theref ore we can say that the number whose 18
72 % is 1.26, is 504.
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C) 1488
Step 1
Lets assume x is the number whose 54
48 % is 16.74.
Step 2
Now we can represents 54
48 % of x is 16.74 as:
x × 54
48 % = 16.74
⇒ x × 54
48 × 100 = 16.74
⇒ x × 5400
48 = 16.74
⇒ x = 16.74 × 48
5400
⇒ x = 1488
Step 3
Theref ore we can say that the number whose 54
48 % is 16.74, is 1488.
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D) 27
Step 1
Lets assume x is the number whose 6
9 % is 0.18.
Step 2
Now we can represents 6
9 % of x is 0.18 as:
x × 6
9 % = 0.18
⇒ x × 6
9 × 100 = 0.18
⇒ x × 600
9 = 0.18
⇒ x = 0.18 × 9
600
⇒ x = 27
Step 3
Theref ore we can say that the number whose 6
9 % is 0.18, is 27.
(15) True
Step 1
According to the question, we have been asked to verif y that 26% of 47% of 1200 = 47%of 26% of 1200 is true or f alse.
Step 2
We need to check if L.H.S. = R.H.S.> 26
100 [
47
100 × 1200] =
47
100 [
26
100 × 1200]
Since, all the terms are being multiplied and are same on both the sides, any order ofmultiplication will give the same result i.e
1466400
10000 =
1466400
10000
L.H.S. = R.H.S.
Step 3
Theref ore, 26% of 47% of 1200 = 47% of 26% of 1200 is true.
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