Ncert Class 6 Mathematics Solutions Chapter 12 Ratio and Proportion
Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of NCERT Class 6 Mathematics Book, Chapter 12, Ratio and Proportion. Here students can easily find step by step solutions of all the problems for Ratio and Proportion, Exercise 12.1, 12.2 and 12.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 12 solutions. Here all the solutions are based on NCERT latest syllabus.
Ratio and Proportion Exercise 12.1 Solution :
(1) There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b) What is the ratio of number of girls to the total number of students in the class?
Solution :
(a) 20 girls and 15 boys in a class.
Ratio of number of girls to the number of boys = 4 : 3
(b) Total number of students = 35
Ratio of number of girls to the total number of students in the class = 4 : 7
(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 number of students liking tennis.
(b) Number of students liking cricket to total number of students.
Solution :
(a) 0 students in a class, 6 like football, 12 like cricket and remaining like tennis
= Ratio of Number of students liking football to number of students liking tennis = 1 : 2
(b) 30 students in a class, 6 like football, 12 like cricket and remaining like tennis.
= Ratio of Number of students liking cricket to total number of students = 2 : 5
(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 :
Distances travelled by Hamid and Akhtar in an hour are 9 km and 12 km.
Ratio of speed of Hamid to the speed of Akhtar = 3 : 4
(5) Fill in the following blanks :
15/18 = _ /6 = 10// = _ /30
Are these equivalent ratios?
Solution :
15/18 = 5/6 = 10/12 = 25/30
Yes, these are equivalent ratios.
(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 :
(a) Ratio of 81 to 108 = 3: 4
(Divided both the numbers by 27)
(b) Ratio of 98 to 63 =14: 9
(Divided both the numbers by 7)
(c) Ratio of 33 km to 121 km = 3: 11
(Divided both the number by 11)
(d) Ratio of 30 minutes to 45 minutes = 2:3
(Divided both the numbers by 15)
(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 Rs 1
(d) 500 mL to 2 litres
Solution :
(a) Here you see both are in different unit – One is minutes and the other is hours.
Students, we have to make it same unit at first.
Here, 1.5 hours = 90 minutes.
So the ratio of 30 minutes to 90 minutes is = 1 : 3
(Divided both the numbers by 30)
(b) We have to make it same unit at first.
Here, 1.5 m = 150 cm
So, the ratio of 40 cm to 150 cm is = 4 : 15
(Divided both the numbers by 10)
(c) 1 rupees = 100 paise
Ratio of 55 paise to 100 paise =11: 20
Here you see both are in different unit – One is paise and the other is rupee.
So Students, we have to make it same unit at first.
Here, 1 rupees = 100 paise
So the ratio of 55 paise to 100 paise = 11: 20
(Divided both the numbers by 5)
(d) 2 Litre = 2000 ml
Ratio of 500 mL to 2000 ml =1 : 4
Here you see both are in different unit – One is litre and the other is ml.
So Students, we have to make it same unit at first.
Here, 2 Litre = 2000 ml
So the ratio of 500 ml to 2000 ml =1 : 4
(Divided both the numbers by)
(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) Seema earns Rs. 1, 50, 000 and saves Rs. 50,000.
Ratio of Money that Seema earns to the money she saves = 3 : 1
(Divided both the numbers by 50,000)
(b) Ratio of Money that she saves to the money she spends = 1 : 2
(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 :
There are 102 teachers in a school of 3300 students.
Ratio of the number of teachers to the number of students = 17 : 550
(Divided both the numbers by 6)
(10) In a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) 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 :
(a) Number of girls to the total number of students.
In a college, out of 4320 students, 2300 are girls.
Ratio of Number of girls to the total number of students = 115 : 216
(b) Number of boys to the number of girls.
Ratio of Number of boys to the number of girls = 101 : 115
(c) Number of boys to the total number of students.
Ratio of Number of boys to the total number of students = 101 : 216
(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
(a) 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 :
(a) Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis.
Ratio of Number of students who opted basketball to the number of students who opted table tennis = 3 : 1
(b) Ratio of Number of students who opted cricket to the number of students opting basketball = 16 : 15
(c) Ratio of Number of students who opted basketball to the total number of students = 5 : 12
(12) Cost of a dozen pens is Rs 180 and cost of 8 ball pens is Rs 56. Find the ratio of the cost of a pen to the cost of a ball pen.
Solution :
The ratio of the cost of a pen to the cost of a ball pen
Cost of a pen
= 180/12
= 15
Cost of a ball pen,
= 56/8
= 7
The ratio of the cost of a pen to the cost of a ball pen = 15 : 7
(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 :
We can complete the table like as follows,
Ratio of breadth and length of a hall is 2 : 5
2/5 = 2 × 5/5 × 2
= 10/25 = 10 x 2/25 x 2
= 20/50
= 20 × 2/50 × 2
= 40/100
(14) Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.
Solution :
Total pens = 20 ratio of 3 : 2.
1 part is 20/5 = 4
∴ Sheela pens = 4 × 3 = 12
∴ Sangeeta pens = 4 × 2 = 8
(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 :
Divide Rs. 36 between her daughters Shreya and Bhoomika in the ratio of their ages.
Age of Shreya is 15 years and age of Bhoomika is 12 years.
Ratio of ages of Shreya and Bhoomika
= 15/12
= 5/4
Divide Rs. 36 between her daughters Shreya and Bhoomika in the ratio of 5/4
1 part is 36 /9 = 4
Shreya will get
= 4 x 5
= Rs. 20
Bhoomika will get
= 4 x 4
= Rs. 16
(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 :
(a) Present age of father to the present age of son.
Present age of father is 42 years and that of his son is 14 years.
Ratio of Present age of father to the present age of son
= 42/14
= 3 : 1
(b) Age of the father to the age of son, when son was 12 years old.
Ratio of Age of the father to the age of son, when son was 12 years old.
When son was 12 years old, father age is 40
Ratio of Age of the father to the age of son, when son was 12 years old
= 40/12
= 20 : 6
(c) Age of father after 10 years to the age of son after 10 years.
Age of father after 10 years
= 42 + 10
= 52
Age of son after 10 years
= 14 + 10
= 24
Ratio of Age of father after 10 years to the age of son after 10 years.
= 52/24
= 13 : 4
(d) Age of father to the age of son when father was 30 years old.
Age of father to the age of son when father was 30 years old
= 42 + 16
= 58
Ratio of Age of father to the age of son when father was 30 years old
= 58/30
= 29 : 15
Ratio and Proportion Exercise 12.2 Solution :
(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 :
(a) a = 15 , b = 45, c = 40 . d = 120
Numbers are in proportion when a x d = b x c
15 x 120 = 1800
45 x 40 = 1800
15 x 120 = 45 x 40
∴ 15, 45, 40, 120 are in proportion.
(b) Let, a = 33, b = 121, c = 9. d = 96
Numbers are in proportion when a x d = b x c
33 x 96 = 3168
121 x 9 = 1089
33 x 96 not equal 121 x 9
∴ 33, 121, 9, 96 are not in proportion.
(c) Let, a = 24, b = 28, c =36 d = 48
Numbers are in proportion when a x d = b x c
24 x 48 = 1152
28 x 36 = 1008
24 x 48 not equal 28 x 36
∴ 24, 28, 36, 48 are not in proportion
(d) Let, a = 32, b = 48, c = 70, d = 210
Numbers are in proportion when a x d = b x c
32 x 210 = 6720
48 x 70 = 3360
32 x 210 not equal 48 x 70
∴ 32, 48, 70, 210 are not in proportion
(e) Let, a = 4 , b = 6, c = 8 , d = 12
Numbers are in proportion when a x d = b x c
4 x 12 = 48
6 x 8 = 48
4 x 12 = 6 x 8
∴ 4, 6, 8, 12 are in proportion
(f) Let, a = 33, b = 44, c = 75 , d = 100
Numbers are in proportion when a x d = b x c
33 x 100 = 3300
44 x 75 = 3300
33 x 100 = 44 x 75
∴ 33, 44, 75, 100 are in proportion
(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) We know, Numbers are in proportion when a x d = b x c
So, 16 x 30 = 480
24 x 20 = 480
16 : 24 :: 20 : 30
Therefore answer is True.
(b) Numbers are in proportion when a x d = b x c
So, 21 x 10 = 210
35 x 6 = 210
21: 6 :: 35 : 10
There fore, the answer is True
(c) Numbers are in proportion when a x d = b x c
So, 12 x 12 = 144
18 x 28 = 504
12 : 18 :: 28 : 12
Therefore, the answer is False
(d) Numbers are in proportion when a x d = b x c
So, 8 x 27 = 216
9 x 24 = 216
8 : 9 :: 24 : 27
Therefore, The answer is True
(e) Numbers are in proportion when a x d = b x c
So, 5.2 x 4 = 20.8
3.9 x 3 = 11.7
5.2 : 3.9 :: 3 : 4
Therefore, the answer is False
(f) Numbers are in proportion when a x d = b x c
So, 0.9 x 4 = 3.6
0.36 x 10 = 3.6
0.9:0.36:: 10 : 4
Therefore, the answer is True
(3) Are the following statements true?
(a) 40 persons : 200 persons = Rs 15 : Rs 75
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
(c) 99 kg : 45 kg = Rs 44 : Rs 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 = 1 : 5
15: 75 = 1 : 5
40 persons : 200 persons = 15 : 75
Therefore the answer is True.
(b) 7.5 litres: 15 litres = 1 : 2
5 kg: 10 kg = 1 : 2
7.5 litres: 15 litres = 5 kg: 10 kg
Therefore, the answer is True.
(c) 99 kg : 45 kg = 11 : 5
44 : 20 = 11 : 5
99 kg : 45 kg = 44 : 20
Therefore, the answer is True.
(d) 32 m : 64 m = 1 : 2
6 sec : 12 sec = 1 : 2
32 m : 64 m = 6 sec : 12 sec
Therefore, the answer is True.
(e) 45 km : 60 km
= 3 : 4
12 hours : 15 hours
= 4 : 5
∴ The given ratio’s are not in proportion.
Hence, 45 km : 60 km = 12 hours : 15 hours
∴ This statement is False.
(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 Rs 40 : Rs 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 litre and Rs 4 : Rs 50
Solution :
(i) 25 cm : 1 m and ₹ 40 : ₹ 160
= 25 : 100 : : 40 : 160
= 25/100 = 40/160
= 1/4 = 1/4
∴ They are in proportion.
(ii) 39 litres : 65 litres and 6 bottles : 10 bottles
= 39 : 65 : : 6 : 10
= 39/65 = 6/10
= 3/5 = 3/5
∴ They are in proportion.
(iii) 200 mL : 2.5 L and ₹ 4 : ₹50
= 200 : 2500 : : 4 : 50
= 200/2500 = 4/50
= 2/2.5 = 2/25
∴ They are in proportion.
(iv) 2 kg : 80 kg and 25 g : 625 kg
= 2 : 80 : : 25 : 625000
= 2/80 = 25/625000
= 1/40 = 1/25000
∴ They are not in proportion.
Ratio and Proportion Exercise 12.3 Solution :
(1) If the cost of 7 m of cloth is Rs 1470, find the cost of 5 m of cloth.
Solution :
Ekta earns 3000 in 10 days
Ekta earns in 1 day
= 3000/10
= Rs.300
Ekta earns in 30 days
= 300 x 30
= 9000
∴ Ekta earns in 30 days is Rs.9000
(3) If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.
Solution :
It has rained 276 mm in the last 3 days.
Rain in 1 day = 276/3 = 92 mm
Rain will fall in one full week
= 92 x 7
= 644 mm.
1 cm = 10 mm.
644 mm. = 64. 4 cm
Rain will fall in one full week is 64. 4 cm.
(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 :
We have given that, the temperature has dropped by 15 degree Celsius in the last 30 days.
Thus, for 30 days = 15 degree Celsius
So for 1 days = 15/30 = 1/2 degree Celsius
Therefore, for 10 days
= 10 × 1/2
= 5 degree Celsius
(6) Shaina pays Rs 15000 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?
Solution :
Shaina pays 15000 as rent for 3 months.
Rent per month = 15000/3 = 5000
She has to pay for a whole year
= 12 x 5000
= 60,000
∴ Shaina has to pay for a whole year is 60,000.
(7) Cost of 4 dozen bananas is 180. How many bananas can be purchased for 90?
Solution :
As per the question,
Cost of 4 dozen bananas is 180
Cost of 1 dozen bananas
= 180/4
= Rs.45
Bananas can be purchased for 90
= 90/45
= 2 Dozen
∴ Bananas can be purchased for 90 is 2 Dozen.
(8) The weight of 72 books is 9 kg. What is the weight of 40 such books?
Solution :
The weight of 72 books is 9 kg
The weight of 1 book
= 9000/72
= 125 g
The weight of 40 such books
= 40 x 125
= 5000 g
= 5 kg.
Hence, the weight of 40 such books is 5 kg
(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 :
A truck requires 108 litres of diesel for covering a distance of 594 km
A truck travel in 1 litre diesel,
= 594/108
= 5.5 km
Diesel will be required by the truck to cover a distance of 1650 km
= 1650/5.5
= 300 litre.
Hence, Diesel will be required by the truck to cover a distance of 1650 km is 300 litre.
(10) Raju purchases 10 pens for Rs 150 and Manish buys 7 pens for Rs 84. Can you say who got the pens cheaper?
Solution :
Raju purchases 10 pens for 150
Price of raju’s pen
= 150/10
= 15
Manish buys 7 pens for 84.
Price of Manish’s pen
= 84/7
= 12
∴ Manish got the pens cheaper.
(11) Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?
Solution :
Anish made 42 runs in 6 overs
Anish runs in 1 over,
= 42/6
= 7 runs.
Anup made 63 runs in 7 overs.
Anup runs in 1 over,
= 63/7
= 9 runs.
∴ Anup made more runs per over.
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