Ratio and Proportion Class 6 Worksheet

Please check Solutions of Ratio and Proportion Class 6 Worksheet at the end of the questions.

Ratio and Proportion Class 6 Worksheet

Ratio and Proportion Class 6 Worksheet

1. Convert the ratio 12 : 60 in its simplest form.
a) 1 : 3
b) 3 : 10
c) 11 : 5
d) 1 : 5

2. Find the ratio of 60 cm to 2.5 m?
a) 7 : 26
b) 9 : 28
c) 5 : 22
d) 6 : 25

3. Find the ratio of 50 g to 2 kg?
a) 1 : 40
b) 4 : 43
c) 1 : 37
d) 2 : 41

4. Find the ratio of 30 min to 3 hours?
a) 2 : 7
b) 4 : 9
c) 1 : 6
d) 1 : 10

5. Find the ratio of 75 paise to ₹ 1.5
a) 2 : 3
b) 4 : 5
c) 1 : 4
d) 1 : 2

6. Find the Equivalent ratio of 5 : 4
a) $\cfrac{21}{12}$
b) $\cfrac{4}{5}$
c) $\cfrac{20}{16}$
d) $\cfrac{18}{12}$

7. Two numbers are in the ratio 2 : 3 and their sum is 75. Find the numbers?
a) 30 and 45
b) 34 and 41
c) 25 and 50
d) 33 and 42

8. Divide ₹ 4500 among X and Y in the ratio 3 : 2
a) X = 2450 , Y = 1950
b) X = 2500 , Y = 2000
c) X = 2700 , Y = 1800
d) X = 2600 , Y = 1900

9. Divide ₹ 1800 among X , Y and Z in the ratio 3 : 4 : 1
a) X = 675 , Y = 900 , Z = 225
b) X = 800 , Y = 675 , Z = 225
c) X = 775 , Y = 1000 , Z = 325
d) X = 675 , Y = 775 , Z = 225

10. Compare the ratios ( 2 : 1 ) and ( 1 : 4 )
a) ( 2 : 1 ) > ( 1 : 4 )
b) ( 2 : 1 ) = ( 1 : 4 )
c) ( 2 : 1 ) < ( 1 : 4 )

11. Find the missing terms $\cfrac{4}{7}$ = $\cfrac{}{35}$
a) 21
b) 19
c) 20
d) 22

12. Find the missing terms:
$\cfrac{56}{104}$ = $\cfrac{}{13}$ = $\cfrac{14}{}$
a) 7, 26
b) 6, 27
c) 8, 27
d) 9, 25

13. Are the ratios 90 cm : 180 cm and 180 m : 340 m in proportion?
a) Yes
b) No

14. Are 6 , 9 , 10 , 15 in proportion?
a) Yes
b) No

15. If 2 : 4 : : y : 6, find the value of y?
a) 4
b) 3
c) 5
d) 6

16. If 4 : y : : y : 16, find the value of y?
a) 8
b) 9
c) 7
d) 10

17. If 2, 12, y are in proportion, find the value of y?
a) 71
b) 73
c) 72
d) 74

18. There are 45 girls and 75 boys in class. Then find the ratio of number of boys to the number of girls?
a) 3 : 2
b) 5 : 3
c) 2 : 4
d) 5 : 6

19. 8 workers can reap a field in 12 days, in how many days can 4 workers reap the same field?
a) 26 days
b) 25 days
c) 24 days
d) 23 days

20. If 12 mangoes cost ₹ 36 , what is the cost of 15 mangoes
a) ₹ 30
b) ₹ 45
c) ₹ 57
d) ₹ 46

21. If a mechanic earns ₹ 2000 at 2 cars. How much he will earn in 1 day, if in a day he receive 12 cars?
a) ₹ 12345
b) ₹ 12000
c) ₹ 12213
d) ₹ 11981

22. If a student pays ₹ 15000 as annual fees to the school. Find his fee per month?
a) ₹ 1250
b) ₹ 1387
c) ₹ 1393
d) ₹ 1225

Ratio and Proportion Class 6 Worksheet Solutions

Ratio and Proportion Class 6 Worksheet – Solution 1

HCF of 12 and 60 is 12
Since, 12 : 60
= $\cfrac{12}{60}$
Dividing Both 12 and 60 by their HCF
= $\cfrac{12 \div 12 }{60 \div 12 }$
= $\cfrac{1}{5}$
= 1 : 5
Hence, the simplest form of 12 : 60 is 1 : 5

Correct Answer – d) 1 : 5

Ratio and Proportion Class 6 Worksheet – Solution 2

Taking both the quantities in same unit, we have
2.5 m = ( 2.5 x 100 ) = 250 cm
The equation now becomes, 60 cm : 250 cm
or
= $\cfrac{60}{250}$
Dividing both the numbers by their HCF, i.e
= $\cfrac{60 \div 10 }{250 \div 10 }$
= $\cfrac{6}{25}$= 6 : 25
Hence, the required ratio is 6 : 25

Correct Answer – d) 6 : 25

Ratio and Proportion Class 6 Worksheet – Solution 3

Taking both the quantities in same unit, we have
2 kg = ( 2 x 1000 ) = 2000 g
The equation now becomes 50 g : 2000 g
or
= $\cfrac{50}{2000}$
Dividing both the numbers by their HCF, i.e 50
= $\cfrac{50 \div 50 }{2000 \div 50 }$
= $\cfrac{1}{40}$= 1 : 40
Hence, the required ratio is 1 : 40

Correct Answer – a) 1 : 40

Ratio and Proportion Class 6 Worksheet – Solution 4

Taking both the quantities in same unit, we have
3 hours = ( 3 x 60 ) = 180 min
The equation now becomes 30 min : 180 min
or
= $\cfrac{30}{180}$
Dividing both the numbers by their HCF, i.e 30
= $\cfrac{30 \div 30 }{180 \div 30 }$
= $\cfrac{1}{6}$= 1 : 6
Hence, the required ratio is 1 : 6

Correct Answer – c) 1 : 6

Ratio and Proportion Class 6 Worksheet – Solution 5

Taking both the quantities in same unit, we have
₹ 1.5 = ( 1.5 x 100 ) = 150 paise
The equation now becomes 75 paise : 150 paise
or
= $\cfrac{75}{150}$
Dividing both the numbers by their HCF, i.e 75
= $\cfrac{75 \div 75 }{150 \div 75 }$
= $\cfrac{1}{2}$= 1 : 2
Hence, the required ratio is 1 : 2

Correct Answer – d) 1 : 2

Ratio and Proportion Class 6 Worksheet – Solution 6

On multiplying or dividing each term of a ratio by the same non zero number, we get a ratio equivalent to the given ratio
For, $\cfrac{20}{16}$
Both numerator and denominator of given fraction is multiplied by same nonzero number i.e 4
$\cfrac {5\times 4 }{ 4\times 4 }$ = $\cfrac{20}{16}$
$\cfrac{20}{16}$is an equivalent ratio of $\cfrac{5}{4}$
$\cfrac{4}{5}$is not an equivalent ratio of $\cfrac{5}{4}$As both 5 and 4 are not multiply by same non zero number
$\cfrac{21}{12}$is not an equivalent ratio of $\cfrac{5}{4}$As both 5 and 4 are not multiply by same non zero number
$\cfrac{18}{12}$is not an equivalent ratio of $\cfrac{5}{4}$As both 5 and 4 are not multiply by same non zero number

Correct Answer – c) $\cfrac{20}{16}$

Ratio and Proportion Class 6 Worksheet – Solution 7

Let the required number be 2a and 3a
Since the sum of these two numbers is given, we can say that
2a + 3a = 75
5a = 75
a = $\cfrac{75}{5}$
a = 15
So, the first number is 2a = 2 x 15
= 30
Second number is 3a = 3 x 15
= 45
Hence, two numbers are 30 and 45

Correct Answer – a) 30 and 45

Ratio and Proportion Class 6 Worksheet – Solution 8

Total money = ₹ 4500
Given ratio = 3 : 2
Sum of ratio terms = ( 3 + 2 )
= 5
Give: $\cfrac{3}{5}$part of ₹ 4500 to X
Give: $\cfrac{2}{5}$part of ₹ 4500 to Y
that is,
X ‘s share = ₹ ( 4500 x $\cfrac{3}{5}$) = ₹ 2700
Y ‘s share = ₹ ( 4500 x $\cfrac{2}{5}$) = ₹ 1800

Correct Answer – c) X = 2700 , Y = 1800

Ratio and Proportion Class 6 Worksheet – Solution 9

Total money = ₹ 1800
Given ratio = 3 : 4 : 1
Sum of ratio terms = ( 3 + 4 + 1 )
= 8
X share = ₹ ( 1800 x $\cfrac{3}{8}$) = ₹ 675
Y share = ₹ ( 1800 x $\cfrac{4}{8}$) = ₹ 900
Z share = ₹ ( 1800 x $\cfrac{1}{8}$) = ₹ 225

Correct Answer – a) X = 675 , Y = 900 , Z = 225

Ratio and Proportion Class 6 Worksheet – Solution 10

We can write
( 2 : 1 ) = $\cfrac{2}{1}$ and ( 1 : 4 ) = $\cfrac{1}{4}$
Now, let us compare $\cfrac{2}{1}$ and $\cfrac{1}{4}$
LCM of 1 and 4 is 4
Making the denominator of each fraction equal to 4
We have, $\cfrac{2}{1}$ = $\cfrac { 2 \times 4 }{ 1\times 4 }$ = $\cfrac{8}{4}$
and $\cfrac{1}{4}$ = $\cfrac { 1 \times 1 }{ 4\times 1 }$ = $\cfrac{1}{4}$
In case of Like fractions, the number whose numerator is greater is larger. Hence we can say $\cfrac{8}{4}$ > $\cfrac{1}{4}$
That is $\cfrac{2}{1}$ > $\cfrac{1}{4}$
Hence, ( 2 : 1 ) > ( 1 : 4 )

Correct Answer – a) ( 2 : 1 ) > ( 1 : 4 )

Ratio and Proportion Class 6 Worksheet – Solution 11

Let $\cfrac{4}{7}$ = $\cfrac{y}{35}$
Then, 4 x 35 = 7y
7y = 4 x 35
y = $\cfrac{4\quad \times \quad35 }{7}$
y = 20
Hence, $\cfrac{4}{7}$ = $\cfrac{20}{35}$

Ratio and Proportion Class 6 Worksheet – Solution 12

Let $\cfrac{56}{104}$ = $\cfrac{y}{13}$
Then, 56 x 13 = 104y
104y = 56 x 13
y = $\cfrac{56 \times 13 }{104}$
y = 7
Since, $\cfrac{56}{104}$ = $\cfrac{7}{13}$
Again, let $\cfrac{7}{13}$ = $\cfrac{14}{z}$
Then, 7z = 14 x 13
z = $\cfrac{14 \times 13 }{7}$
z = $\cfrac{182}{7}$
z = 26
Since, $\cfrac{7}{13}$ = $\cfrac{14}{26}$
Hence, $\cfrac{56}{104}$ = $\cfrac{7}{13}$ = $\cfrac{14}{26}$

Correct Answer – a) 7 , 26

Ratio and Proportion Class 6 Worksheet – Solution 13

We have 90 cm : 180 cm
= 90 : 180
= $\cfrac{90}{180}$
=$\cfrac{90 \div 90 }{180 \div 90 }$(HCF of 90 and 180 is 90 )
= $\cfrac{1}{2}$
180 m : 340 m
= 180 : 340
= $\cfrac{180}{340}$
=$\cfrac{180 \div 20 }{340 \div 20 }$( HCF of 180 and 340 is 20 )
= $\cfrac{9}{17}$
Since, the ratios 90 cm : 180 cm and 180 m : 340 m are equal to $\cfrac{1}{2}$ and $\cfrac{9}{17}$ . So, they are not in proportion.

Ratio and Proportion Class 6 Worksheet – Solution 14

We have, 6 : 9 = $\cfrac{6}{9}$ = $\cfrac{6 \div 3 }{9 \div 3 }$= $\cfrac{2}{3}$
and 10 : 15 = $\cfrac{10}{15}$ = $\cfrac{10 \div 5 }{15 \div 5 }$= $\cfrac{2}{3}$
Since, 6 : 9 = 10 : 15
Hence, 6 , 9 , 10 , 15 are in Proportion
Alternative method: Product of extremes = Product of means
Here, Means are 9 and 10
Extremes are 6 and 15
Product of extremes = 6 x 15 = 90
Product of means = 9 x 10 = 90
Since, Product of extremes = Product of means
Hence, 6 , 9 , 10 , 15 are in Proportion

Ratio and Proportion Class 6 Worksheet – Solution 15

We know that, Product of means = Product of extremes
In the given numbers, we can say that 4 , y are means and 2 , 6 are extremes
4 x y = 2 x 6
y = $\cfrac{2\quad \times \quad6 }{4}$
y = 3
Hence, y = 3

Ratio and Proportion Class 6 Worksheet – Solution 16

Clearly, Product of means = Product of extremes
y x y = 4 x 16
${ y }^{ 2 }$ = 4 x 16
${ y }^{ 2 }$ = 64
Hence, y = 8

Ratio and Proportion Class 6 Worksheet – Solution 17

2 , 12 , y are in proportion
Which means 2 , 12 , 12 , y are in proportion
i.e, 2 : 12 : : 12 : y
Product of means = Product of extremes
here,
means = 12 and 12
extremes = 2 and y
12 x 12 = 2 x y
144 = 2 x y
y = $\cfrac{144}{2}$
Hence, y = 72

Ratio and Proportion Class 6 Worksheet – Solution 18

$\cfrac { Number\quad of\quad \quad boys }{ Number\quad of\quad girls}$ = $\cfrac{75}{45}$
On simplifying,
$\cfrac { Number\quad of\quad \quad boys }{ Number\quad of\quad girls}$ = $\cfrac{75 \div 15 }{45 \div 15 }$( HCF of 75 and 45 is 15 )
= $\cfrac{5}{3}$= 5 : 3
Hence,the ratio is 5 : 3

Correct Answer – b) 5 : 3

Ratio and Proportion Class 6 Worksheet – Solution 19

Clearly, less workers will take the more days.
And, more workers will take less days.
8 workers can reap a field in = 12 days
1 worker can reap a field in = ( 12 x 8 ) days
Hence, 4 workers can reap a field in = $\cfrac{12 \times 8 }{4}$days = 24 days
Hence, 4 workers can reap a field in 24 days

Correct Answer – c) 24 days

Ratio and Proportion Class 6 Worksheet – Solution 20

Cost of 12 mangoes = ₹ 36
Cost of 1 mango = ₹ $\cfrac{36}{12}$
Cost of 15 mangoes = ₹ $\cfrac{36\times 15 }{12}$
= ₹ 45

Correct Answer – b) ₹ 45

Ratio and Proportion Class 6 Worksheet – Solution 21

Earning on 2 cars = ₹ 2000
1 car = ₹ $\cfrac{2000}{2}$ = ₹ 1000
Earning on 12 cars = ₹ ( 1000 x 12 )
= ₹ 12000

Correct Answer – b) ₹ 12000

Ratio and Proportion Class 6 Worksheet – Solution 22

Annually means 1 year = 12 months
Fees of 12 month = ₹ 15000
Fees of 1 month = ₹ $\cfrac{15000}{12}$
= ₹ 1250

Correct Answer – a) ₹ 1250