Percentage Grade 6

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 :



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.



(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)



= 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 .



B) 0.4865

Step 1


percentage 4813



4813

20 % =

973

20 %

Step 2




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.



C) 0.798

Step 1


percentage 794



794

5 % =

399

5 %

Step 2


5 % into the simple


399

5 %

= 399

5 × 100

= 399

500

= 0.798

Step 3




D) 0.9065

Step 1


percentage 9013



9013

20 % =

1813

20 %

Step 2




1813

20 %

= 1813

20 × 100

= 1813

2000

= 0.9065

Step 3




E) 0.384

Step 1


percentage 382



382

5 % =

192

5 %

Step 2


5 % into the simple


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 .



F) 0.045

Step 1


percentage 41



41

2 % =

9

2 %

Step 2


2 % into the simple


9

2 %

= 9

2 × 100

= 9

200

= 0.045

Step 3




(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%



(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.



(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



(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.



(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.



(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




C) 7

Step 1


7:100 = 7

100 × 100 %

= 700

100

= 7 %

Step 2


D) 31

Step 1


31:100 = 31

100 × 100 %

= 3100

100

= 31 %

Step 2




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


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




(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


Step 2


⇒ x × 32

100 = 3.84

⇒ x = 3.84 × 100

32

⇒ x = 384

32

⇒ x = 12

Step 3




C) 7

Step 1


Step 2


⇒ 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


Step 2


⇒ x × 37

100 = 1.11

⇒ x = 1.11 × 100

37

⇒ x = 111

37

⇒ x = 3

Step 3




(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.



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..



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.



(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.



B) 504

Step 1


72 % is 1.26.

Step 2


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


72 % is 1.26, is 504.



C) 1488

Step 1


48 % is 16.74.

Step 2


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


48 % is 16.74, is 1488.



D) 27

Step 1


9 % is 0.18.

Step 2


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


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.



Percentage Grade 6

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