# Class 6 Maths Chapter 12 Ratios and Proportions

Exercise 12.1

Ex 12.1 Class 6 Maths Question 1.
There are 20 girls and 15 boys in a class.
(a) What is the ratio of the number of girls to the number of boys?
(b) What is the ratio of the number of girls to the number of students in the class?
Solution:
(a) Number of girls = 20
Number of boys = 15
Total number of students = 20 + 15 = 35
∴ Ratio of the number of girls to the number of boys Thus, the required ratio is 4 : 3.
(b) Ratio of the number of girls to the number of students Thus, the required ratio is 4 : 7.

Ex 12.1 Class 6 Maths Question 2.
Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
(a) Number of students liking football to the number of students liking tennis.
(b) Number of students liking cricket to total number of students. Solution:
Number of students in the class = 30
Number of students liking football = 6
Number of students liking cricket = 12
Number of students liking tennis = 30 – (6 + 12) = 30 – 18 = 12

(a) Ratio of the number of the students liking football to the number of students liking tennis Thus, the required ratio is 1 : 2.

(b) Ratio of the number of students liking cricket to the total number of students Thus, the required ratio is 2 : 5.

Ex 12.1 Class 6 Maths Question 3.
See the figure and find the ratio of
(а) Number of triangles to the number of circles inside the rectangle.
(b) Number of squares to all the figures inside the rectangle.
(c) Number of circles to all the figures inside the rectangle. Solution:
(a) Number of triangles 3
Number of circles = 2
∴ Ratio of number of triangles to the number of circles Thus, the required ratio is 3 : 2.

(b) Number of squares = 2
Number of all figures = 7
∴ Ratio of number of squares to the number of all the figures Thus, the required ratio is 2 : 7.

(c) Ratio of number of circles to the number of all the figures Thus, the required ratio is 2 : 7.

Ex 12.1 Class 6 Maths Question 4.
Distances travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of speed of Hamid to the speed of Akhtar.
Solution:
Distance travelled by Hamid = 9 km.
Distance travelled by Akhtar = 12 km.
Speed of Hamid = 9 km
per hour Speed of Akhtar = 12 km per hour
∴ Ratio of the speed of Hamid to the speed of Speed of Hamid ar = Speed of Akhtar Thus, the required ratio is 3 : 4.

Ex 12.1 Class 6 Maths Question 5.
Fill in the following blanks: [Are these equivalent ratios?]
Solution:  Now the fractions, we have Ex 12.1 Class 6 Maths Question 6.
Find the ratio of the following:
(a) 81 to 108
(b) 98 to 63
(c) 33 km to 121 km
(d) 30 minutes to 45 minutes
Solution: Ex 12.1 Class 6 Maths Question 7.
Find the ratio of the following:
(a) 30 minutes to 1.5 hours
(b) 40 cm to 1.5 m
(c) 55 paise to ₹ 1
(d) 500 mL to 2 litres
Solution:
(a) 1 hour = 60 minutes
∴ 1.5 hours = 60 x 1.5 minutes = 90 minutes
∴ Ratio of 30 minutes to 1.5 hours = Ratio of 30 minutes to 90 minutes (b) 1 m = 100 cm
∴ 1.5 m = 1.5 x 100 cm = 150 cm.
∴ Ratio of 40 cm to 1.5 m = Ratio of 40 cm to 150 cm. (c) ₹1 = 100 paise
∴ Ratio of 55 paise to ₹ 1 = Ratio of 55 paise to 100 paise (d) 500 mL to 2 litres
1 litre = 1000 mL
∴ 2 litres = 2 x 1000 mL = 2000 mL
∴ Ratio of 500 mL to 2 litres = Ratio of 500 mL to 2000 mL Ex 12.1 Class 6 Maths Question 8.
In a year, Seema earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of
(a) Money that Seema earns to the money she saves.
(b) Money that she saves to the money she spends.
Solution:
(a) Money earned by Seema = ₹ 1,50,000
Money saved by her = ₹ 50,000
∴ Money spent by her = ₹ 1,50,000 – ₹ 50,000 = ₹ 1,00,000
∴ Ratio of money earned by Seema to the money saved by her (b) Ratio of money saved by Seema to the money Ex 12.1 Class 6 Maths Question 9.
There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.
Solution:
Number of teachers = 102
Number of students = 3300
∴ Ratio of number of teachers to the number of students Ex 12.1 Class 6 Maths Question 10.
In a college, out of 4320 students, 2300 are girls, find the ratio of
(а) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.
Solution:
Total number of students = 4320
Number of girls = 2300
∴ Number of boys = 4320 – 2300 = 2020

(a) Ratio of number of girls to the total number of students (b) Ratio of number of boys to the number of girls (c) Ratio of number of boys to the total number of students Ex 12.1 Class 6 Maths Question 11.
Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of
(а) Number of students who opted basketball to the number of students who opted table tennis.
(b) Number of students who opted cricket to the number of students opting basketball.
(c) Number of students who opted basketball to the total number of students.
Solution:
Total number of students = 1800
Number of students opting basketball = 750
Number of students who opted cricket = 800
Number of remaining students who opted table tennis = 1800 – (750 + 800)
= 1800 – 1550 = 250

(а) Ratio of number of students opted basketball to the number of students who opted table tennis
Number of students opting basketball Number of students opting table tennis (b) Ratio of the students who opted cricket to the number of students opting basketball (c) Ratio of number of students who opted basketball to the total number of students Ex 12.1 Class 6 Maths Question 12.
Cost of a dozen pens is ₹180 and cost of 8 ball pens is ₹56. Find the ratio of the cost of a pen to the cost of a ball pen.
Solution:
Cost of 1 dozen, i.e., 12 pens = ₹180
∴ Cost of 1 pen = ₹18012 = ₹15
Cost of 8 ball pens = ₹56
∴ Cost of 1 ball pen = ₹ 568 = ₹ 7
Ratio of cost of 1 pen to cost of 1 ball pen Thus required ratio is 15 : 7.

Ex 12.1 Class 6 Maths Question 13.
Consider the statement : Ratio of breadth and length of a hall is 2 : 5. Complete the following table that shows some possible breadths and lengths of the hall. Solution: Ex 12.1 Class 6 Maths Question 14.
Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.
Solution:
We have 3 + 2 = 5
Total number of pen = 20
∴ Sheela’s share = 35 x 20 = 3 x 4 = 12 pens 5
Sangeeta’s shares = 25 x 20 = 2 x 4 = 8 pens.
Thus Sheela gets 12 pens and Sangeeta gets 8 pens.

Ex 12.1 Class 6 Maths Question 15.
Mother wants to divide ₹ 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get?
Solution:
Given that:
Money got by Shreya : Money got by Bhoomika = 15 : 12
∴ Sum = 15 + 12 = 27 Ex 12.1 Class 6 Maths Question 16.
Present age of father is 42 years and that of his son is 14 years. Find the ratio of
(a) Present age of father to the present age of son.
(b) Age of the father to the age of son, when son was 12 years old.
(c) Age of father after 10 years to the age of son after 10 years.
(d) Age of father to the age of son when father was 30 years old.
Solution:
Present age of father = 42 years.
Present age of his son = 14 years.
(a) Ratio of present age of father to the present age of son (b) When son was 12 years old, i.e., 14 – 12 = 2 years ago father’s age = 42 – 2 = 40 years.
Ratio of the father’s age to the son’s age (c) Ratio of father’s age after 10 years, i.e., 42 + 10 = 52 years
to the age of son after 10 years, i.e., = 14 + 10 = 24 years (d) Ratio of the son’s age to the age of father when he was only 30 years .
When father was 30 years,
i.e., before 42 – 30 = 12 years
Age of son was = 14 – 12 = 2 years
∴ Required ratio Exercise 12.2

Ex 12.2 Class 6 Maths Question 1.
Determine if the following are in proportion,
(a) 15, 45, 40, 120
(b) 33, 121, 9, 96
(c) 24, 28, 36, 48
(d) 32, 48, 70, 210
(e) 4, 6, 8, 12
(f) 33, 44, 75, 100
Solution: ∴ 15 : 45 :: 40 : 120
∴ 15, 45, 40 and 120 are in proportion. ∴ 33, 121, 9 and 96 are in proportion. ∴ 24, 28, 36 and 48 are not in proportion. Since 23 ≠ 13
∴ 32, 48, 70 and 210 are not in proportion. 4 ∴ 4 : 6 :: 8 : 12
∴ 4, 6, 8 and 12 are in proportion. ∴ 33 : 44 : : 75 : 100
∴ 33, 44, 75 and 100 are in proportion.

Ex 12.2 Class 6 Maths Question 2.
Write True (T) or False (F) against each of the following statements:
(a) 16 : 24 :: 20 : 30
(b) 21 : 6 :: 35 : 10
(c) 12 : 18 :: 28 : 12
(d) 8 : 9 :: 24 : 27
(e) 5.2 : 3.9 :: 3 : 4
(f) 0.9 : 0.36 :: 10 : 4
Solution:
(a) 16 : 24 :: 20 : 30
Product of the extreme terms = 16 x 30 = 480
Product of the middle terms = 24 x 20 = 480
∴ The given statement (a) → (T)

(b) 21 : 6 :: 35 : 10
Product of the extreme terms = 21 x 10 = 210
Product of the middle terms = 6 x 35 = 210
∴ The given statement (b) → (T)

(c) 12 : 18 :: 28 : 12
Product of the extreme terms = 12 x 12 = 144
Product of the middle terms = 18 x 28 = 504
Since 144 ≠ 504
∴ The given statement (c) → (F)

(d) 8 : 9 :: 24 : 27
Product of the extreme terms = 8 x 27 = 216
The product of the middle terms = 9 x 24 = 216
The given statement (d) → (T)

(e) 5.2 : 3.9 :: 3 : 4
Product of the extreme terms = 5.2 x 4 = 20.8
Product of the middle terms = 3.9 x 3 = 11.7
Since 20.8 ≠ 11.7
The given statement (e) → (F)

(f) 0.9 : 0.36 :: 10 : 4
Product of the extreme terms = 0.9 x 4 = 3.6
Product of the middle terms = 0.36 x 10 = 3.6
∴ The given statement (f) → (T)

Ex 12.2 Class 6 Maths Question 3.
Are the following statements true?
(a) 40 persons : 200 persons = ₹15 : ₹75
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
(c) 99 kg : 45 kg = ₹ 44 : ₹ 20
(d) 32 m : 64 m = 6 sec : 12 sec
(e) 45 km : 60 km = 12 hours : 15 hours
Solution:
(a) 40 persons : 200 persons ∴ Statement (a) is true.

(b) 7.5 litres : 15 litres ∴ Statement (b) is true. ∴ Statement (c) is true. ∴ Statement (d) is true. ∴ Statement (e) is not true.

Ex 12.2 Class 6 Maths Question 4.
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm : 1 m and ₹ 40 : ₹ 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
(c) 2 kg : 80 kg and 25 g : 625 g
(d) 200 mL : 2.5 litres and ₹ 4 : ₹ 50
Solution:
(a) 25 cm : 1 m = 25 cm : 100 cm [∵ 1 m = 100 cm] ∴ The given ratios are in proportion.
Extreme terms are 25 cm and ₹ 160.
Middle terms are 1 m and ₹40. ∴ The given ratios are in proportion.
Extreme terms are 39 litres and 10 bottles.
Middle terms are 65 litres and 6 bottles. ∴ The given ratios are not in proportion.

(d) 200 mL : 2.5 litres = 2.5 litres = 2.5 x 1000 mL = 2500 mL ∴ The given ratios are in proportion.
Extreme terms are 200 mL and ₹ 50
Middle terms are 2.5 litres and ₹ 4.

Exercise 12.3

Ex 12.3 Class 6 Maths Question 1.
If the cost of 7 m of cloth is ₹ 294, find the cost of 5 m of cloth.
Solution:
Using unitary method, we have cost of 7 m of cloth = ₹294
Cost of 1 m of cloth = ₹ 2947
Cost of 5 m of cloth = ₹(2947 x 5) = ₹(42 x 5)
= ₹ 210
Thus, the required cost = ₹ 210

Ex 12.3 Class 6 Maths Question 2.
Ekta earns ₹ 1500 in 10 days. How much she will earn in 30 days?
Solution:
In 10 days Ekta earn ₹ 1500
In 1 days Ekta will earn ₹ 150010
In 30 days Ekta will earn ₹150010 x 30 = ₹4500
Thus the money earned by Ekta in 30 days = ₹4500.

Ex 12.3 Class 6 Maths Question 3.
If it has rained 276 mm in the last 3 days, how many centimeters of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.
Solution:
In last 3 days the rain falls = 276 mm .
In 1 day the rain falls = 2763mm.
in 7 days the rain will fall = 2763 x 7 mm.
= 92 x 7 mm = 644 mm or 64.4 cm [∵ 1 cm = 10 mm]
Thus, the amount of rain fall in week = 64.4 cm.

Ex 12.3 Class 6 Maths Question 4.
Cost of 5 kg of wheat is ₹ 30.50.
(a) What will be the cost of 8 kg of wheat?
(b) What quantity of wheat can be purchased in ₹ 61?
Solution:
(a) Cost of 5 kg of wheat = ₹ 30.50
Cost of 1 kg of wheat = ₹ 30.505
Cost of 8 kg of wheat = ₹( 30.505 x 8)
= ₹ 48.80
Thus, the required cost = ₹ 48.80

(b) The quantity of wheat purchased in ₹ 30.50 = 5 kg
The quantity of wheat purchased in ₹ 1 = 530.50 kg
The quantity of wheat purchased in ₹ 61 = 5×6130.50 kg
Thus, the required quantity of wheat = 10 kg

Ex 12.3 Class 6 Maths Question 5.
The temperature dropped 15 degree Celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?
Solution:
In last 3,0 days the quantity of drop in temperature = 15 degree Celsius
In last 1 day the quantity of drop in temperature = 1530 degree Celsius
In last 10 days the quantity of drop is temperature = 1530 x 10 degree Celsius
= 5 degree Celsius
Thus the required drop in temperature in last 10 days = 5 degree Celsius.

Ex 12.3 Class 6 Maths Question 6.
Shaina pays ₹ 7500 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?
Solution:
Amount of rent paid in 3 months = ₹ 7500
Amount of rent paid in 1 month = ₹ 75003
Amount of rent paid in 12 months = ₹ ( 75003 x 12)
= ₹ 30,000
Thus the required amount of rent paid in 1 year = ₹ 30,000.

Ex 12.3 Class 6 Maths Question 7.
Cost of 4 dozen bananas is ₹ 60. How many bananas can be purchased for ₹ 12.50?
Solution:
∵ 1 dozen = 12 units
∴ 4 dozen of bananas = 12 x 4 = 48 bananas
₹ 60 is the cost of 4 dozen = 4 x 12 = 48 bananas
₹ 1 is the cost of = 4860 bananas 60.
₹ 12.50 is the cost of = 60060bananas
= 10 bananas
Thus the required number of bananas = 10

Ex 12.3 Class 6 Maths Question 8.
The weight of 72 books is 9 kg. What is the weight of 40 such books?
Solution:
Weight of 72 books = 9 kg
Weight of 1 books = 972kg
Weight of 40 books = 972 x 40 kg = 5 kg
Hence, the required weight = 5 kg.

Ex 12.3 Class 6 Maths Question 9.
A truck requires 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?
Solution:
To cover 594 km, the amount of diesel required = 108 litres.
To cover 1 km, the amount of diesel will be , required = 108594 litres
To cover 1650 km, the amount of diesel required = 108×1650594 litres = 300 litres
Thus, the required amount of diesel = 300 litres.

Ex 12.3 Class 6 Maths Question 10.
Raju purchases 10 pens for ₹150 and Manish buys 7 pens for ₹ 84. Can you say who got the pens cheaper?
Solution:
For Raju,
Cost of 10 pen = ₹150
Cost of 1 pen = ₹ 15010 = ₹ 15
For Manish,
Cost of 7 pens = ₹ 84
Cost of 1 pen = ₹ 847 = ₹12
∴ ₹ 12 < ₹ 15 Thus Manish got the pens cheaper than Raju.

Ex 12.3 Class 6 Maths Question 11.
Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?
Solution:
Number of runs made by Anish in 6 overs = 42
Number of runs made by him in 1 over = 426 = 7 runs.
Number of runs made by Anup in 7 overs = 63
Number of runs made by him in 1 over = 637 = 9 runs.
∴ 9 runs > 7 runs.
Thus, Anup has made more runs.

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