GetStudySolution

Getstudysolution is an online educational platform that allows students to access quality educational services and study materials at no cost.

NCERT Solutions for class 6 Maths chapter 12 – Ratio and Proportion

Back Exercise

Exercise 12.1

Question 1.
There are 20 girls and 15 boys in a class.
(a) What is the ratio of a number of girls to the number of boys?
(b) What is the ratio of a number of girls to the total number of students in the class?
Solution :
(a) Ratio of number of girls to the number of boys

(b) Total number of students in the class = 20 + 15 = 35
∴ Ratio of number of girls to the total number of students in the class

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 a number of students liking tennis.
(b) Number of students liking cricket to the total number of students.
Solution :
(a) Number of students liking tennis = 30-(6+ 12) = 30 – 18 = 12
∴ Ratio of number of students liking football to number of students liking tennis

(b) Number of students liking cricket to total number of students

Question 3.
See the figure and find the ratio of:
(a) 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 triangle inside the rectangle = 3 . , Number of circles inside the rectangle = 2 Ratio of number of triangles to the number of circles inside the rectangle = $\frac{ 3 }{ 2 }$ =3:2.
(b) Number of squares inside the rectangle = 2 Number of all the figures inside the rectangle = 7
∴ Ratio of number of squares to all the figures 2
inside the rectangle = $\frac{ 2 }{ 7 }$ =2:7.
(c) Ratio of number of circles to all the figures inside the rectangle = $\frac{ 2 }{ 7 }$ =2:1.

Question 4.
Distance 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 :
Ratio of speed of Hamid to the speed of

Question 5.
Fill in the following blanks:

Solution :

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 :

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) 1.5 hours = 1.5 × 60 minutes = 90 minutes

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 that she spends.
Solution :
(a) Ratio of money that Seema earns to the money she saves

(b) Money that she spends
= ₹ 1,50,000 – ₹ 50,000 = ₹ 1,00,000
∴ Ratio of money she saves to the money she spends

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 :
Ratio of the number of teachers to the number of students

Question 10.
In a college, out of4320 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) Ratio of number of girls to the total number of students

(b) Number of boys = 4320 – 2300 = 2020
∴ Ratio of number of boys to the number of girl

(c) Ratio of number of boys to the total number of students

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:
(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) Number of students opting table tennis = 1800 – (750 + 800) = 1800 -1550 = 250
∴ Ratio of number of students opting basketball to number of students opting table tennis

(b) Ratio of number of students opting cricket to the number of students opting basketball

(c) Ratio of number of students opting basketball to the total number of students

Question 12.
Cost of a dozen pens is ₹ 180 and cost of 8 ball pens is ₹ 56. Find the ratio of cost of a pen to the cost of a ball pen.
Solution :
1 dozen =12 items
∴ Cost of 12 pens = ₹ 180
∴ Cost of 1 pen = ₹ $\frac{ 180 }{ 12 }$ = ₹ 15
∴ Cost of 8 ball pens = ₹ 56
∴ Cost of 1 ball pen = ₹ $\frac{ 56 }{ 8 }$ = ₹ 7
∴ Ratio of cost of a pen to the cost of a ball 15 pen = $\frac{ 15 }{ 7 }$ =15:7.

Question 13.
Consider the statement: Ratio of breadth and length of a hall 2: 5. Complete the following table that shows some possible breadths and lengths of the hall.

Solution :

Hence, the completed table is as follows:

Question 14.
Divide 20 pens between Sheela and Sangeeta in the ratio 3: 2.
Solution :
Total number of pens = 20 Ratio = 3:2
Sum of the parts = 3 + 2 = 5
∴ Sheel’s shae = $\frac{ 3 }{ 5 }$ × 20 = 12 and, Samgeeta’s share = $\frac{ 2 }{ 5 }$ × 20 = 8

Question 15.
Mother wants to divide ₹ 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If the age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get?
Solution :
Total money = ₹ 36
The ratio of the ages of Shreya and Bhoomika



Hence, Shreya will get ₹ 20 and Bhoomika will get ₹ 16.

Question 16.
Present age of the 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 the son.
(b) Age of the father to the age of son, when the 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) Ratio of the present age of father to the present age of the son

(b) Son was 12 years old 14 – 12 = 2 years before
Age of the father 2 years before = 42 – 2 = 40 years
∴ Ratio of the age of the father to the age of the son. when son was 12 years old

(c) Age of father after 10 years = 42 + 10 = 52 years
Age of son after 10 years = 14 + 10 = 24 years
∴ Ratio of age of father after 10 years to the age of son after 10 years

(d) Father was 30 years old 42 – 30 = 12 years before
Age of son 12 years before = 14 – 12 = 2 years
∴ Ratio of the age of father to the age of son when father was 30 years old

Exercise 12.2

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 :





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 :




Question 3.
Are the following statements true₹ I
(a) 40 Persons : 200 Persons =₹ 15: ₹75 ;
(b) 7.5 litre : 15 litre = 5 kg : 10 kg 1
(c) 99 kg : 45 kg = f 44 : ₹20
(d) 32 m : 64 m = 6 sec: 12 sec
(e) 45 km: 60 km = 12 hours : 15 hours.
Solution :


Since the two ratios are equal, therefore, the given statement is true.

Since the two ratios are equal, therefore, the given statement is true.

Since, the two ratios are equal, therefore, the given statement is true.


Since the two ratios are equal, therefore the given statement is true.

Since the two ratios are not equal, therefore the given statement is false.

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 7 40 : 7160
(b) 39 litre : 65 litre and 6 bottle : 10 bottle
(c) 2 kg : 80 kg and 25 g : 625 g
(d) 200 ml: 2.5 litre and ₹4 ; ₹ 50.
Solution :
(a)
∴ 1 m= 100 cm

Since the two ratios are equal, therefore, the given ratios are in proportion. Middle terms are 1 m and ₹ 40. Extreme terms are 25 cm and ₹ 160.

Since the two ratios are equal, therefore, the given ratios are in proportion. Middle terms are 65 liters and 6 bottles. Extreme terms are 39 liters and 10 bottles.


Since the two ratios are not equal, therefore, the given ratios are not in proportion.

Since the two ratios are equal, therefore, the given ratios are in proportion. Middle terms are 2.5 litres and ₹ 4. Extreme terms are 200 ml and ₹ 50.

Exercise 12.3

Question 1.
If the cost of 7 m of cloth is ₹294, find the cost of 5 m of cloth.
Solution :

Hence, the cost of 5 m of cloth is ₹ 210.

Question 2.
Ekta earns ₹ 1500 in 10 days. How much will she earn in 30 days?
Solution :

Hence, Ekta will earn ₹ 4500 in 30 days.

Question 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 :

Hence, 644 mm = cm = 64.4 cm of rain will fall in one full week (7 days).

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

Hence, the cost of 8 kg of wheat will be ₹ 48.80
(b) In ₹ 30.50, the quantity of wheat that can be purchased = 5 kg

Hence, 10 kg of wheat can be purchased in

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 :
∴ Drop in temperature in 30 days =15 degrees

Hence, the temperature will drop 5 degrees in the next ten days.

Question 6.
Shaina pays ₹ 7500 as rent for 3 months. How much does she have to pay for a whole year, if the rent per month remains same₹
Solution :
∴ 1 Year = 12 months Y
∴ Rent paid by Shaina for 3 months = ₹ 7500
∴ Rent paid by Shaina for 1 month
₹ $\frac{ 7500 }{ 3 }$ = ₹ 2500
∴ Rent paid by Shaina for 12 months = ₹ (2500 x 12) = ₹ 30,000
Hence, Shaina will have to pay ₹ 30,000 for a whole year.

Question 7.
Cost of 4 dozens of bananas is ₹ 60. How many bananas can be purchased for ₹ 12.50?
Solution :
1 dozen = 12 items
∴ 4 dozens =12 x 4 items = 48 items
∴ Number of bananas that can be purchased for ₹60 = 48
∴ Number of bananas that can be pruchased for ₹ 1 = $\frac{ 48 }{ 60 }$
∴ Number of bananas that can be pruchased for ₹ 12.50 = $\frac{ 48 }{ 60 }$ × 12.50 = 10
Hence, 10 bananas can be purchased for ₹ 12.50.

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 = $\frac{ 9 }{ 72 }$ kg  = $\frac{ 1 }{ 8 }$ kg
∴ Weight of 40 books = $\frac{ 1 }{ 8 }$ kg ×40 kg = 5 kg
Hence, the weight of 4(f such books is 5 kg.

Question 9.
A truck requires 108 liters of diesel for covering a distance of594 km. How much diesel will be required by the truck to cover a distance of 1650 km₹
Solution :
∴ Diesel required for covering a distance of 594 km =108 liters
∴ Diesel required for covering a distance of
1 km = $\frac{ 108 }{ 594 }$ litre
∴ Diesel required for covering a distance of
1650 km = $\frac{ 108 }{ 594 }$ × 1650 litres = 300
Hence, 300 liters of diesel will be required by the truck to cover a distance of 1650 km.

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 pens = ₹ 150
∴ Cost of 1 pen = ₹ $\frac{ 150 }{ 10 }$ = ₹ 15

For Manish
∵ Cost of 7 pens = ₹ 84
∴ Cost of 1 pen = ₹ $\frac{ 84 }{ 7 }$ = ₹ 12 7
So, Manish got the pens cheaper.

Question 11.
Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?
Solution :
For Anish
∵ Runs made in 6 overs = 42
∴ Runs made per over = $\frac{ 42 }{ 6 }$ = 7

For Anup
∵ Runs made in 7 overs = 63
∴ Runs made per over = $\frac{ 63 }{ 7 }$ = 9
So, Anup made more runs per over.

In-Text Questions