Class
6 Maths NCERT Solutions
Chapter
12 Ratio and Proportions
Exercise 12.1
Q.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?
Ans :
Number of girls = 20
Number of boys = 15
Total number of students = 20 + 15 = 35
(a) Ratio of number of girls to boys =
(b) Ratio of number of girls to total
students =
Q.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.
Ans :
Number of students who like football =
6
Number of students who like cricket =
12
Number of students who like tennis = 30
− 6 − 12 = 12
(a) Ratio of the number of students
liking football to the number of students liking tennis =
(b) Ratio of the number of students
liking cricket to the total number of students =
Q.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.
Ans :
Number of triangles = 3
Number of circles = 2
Number of squares = 2
Total number of figures = 7
(a) Ratio of the number of triangles to
the number of circles =
(b) Ratio of the number of squares to
all the figures in the rectangle =
(c) Ratio of the number of circles to
all the figures in the rectangle =
Q.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.
Ans :
The distance travelled in an hour by a
certain object is called the speed of that object.
Distance travelled by Hamid in one hour
= 9 km
Distance travelled by Akhtar in one
hour = 12 km
Hamid’s speed = 9 km/hr
Akhtar’s speed = 12 km/hr
Q.5 : Fill in the following blanks :
[Are these equivalent ratios?]
Ans :
Therefore, 5, 12, 25 will come in the
blanks respectively.
Yes, all these are equivalent ratios.
Q.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
Ans :
(a) 
(b) 
(c) 
(d) 
Q.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
Ans :
(a) 30 min =
Required ratio =
(b) 40 cm to 1.5 m
1.5 m = 150 cm
Required ratio =
(c) 55 paise to Re 1
Re 1 = 100 paise
Required ratio =
(d) 500 mL to 2l
1l = 1000 mL
2l = 2000 mL
Required ratio = 
Q.8 : In a year, Seema earns Rs 1, 50, 000
and saves Rs 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.
Ans :
Money earned = Rs 150000
Money saved = Rs 50000
Money spent = Rs 150000 − Rs
50000 = Rs 100000
(a) Ratio of money earned to money
saved =
(b) Ratio of money saved to money spent
=
Q.9 : There are 102 teachers in a school of
3300 students. Find the ratio of the number of teachers to the number of
students.
Ans :
Ratio required =
Q.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.
Ans :
Total number of students = 4320
Number of girls = 2300
Number of boys = 4320 − 2300 =
2020
(a) Required ratio =
(b) Required ratio =
(c) Required ratio =
Q.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.
Ans :
(a) Required ratio =
(b) Required ratio =
(c) Required ratio =
Q.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.
Ans :
Cost of a dozen pens = Rs 180
Cost of 1 pen =
Cost of 8 ball pens = Rs 56
Cost of a ball pen =
Required ratio =
Q.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.
|
Breadth of
the hall (in metres) |
10 |
? |
40 |
|
Length of
the hall (in metres) |
25 |
50 |
? |
Ans :
(i) Length = 50 m
5 × Breadth = 50 × 2 (By
cross-multiplication)
Breadth = 20 m
(ii) Breadth = 40 m
2 × Length = 5 × 40 (By
cross-multiplication)
Length = 100 m
Q.14 : Divide 20 pens between Sheela and
Sangeeta in the ratio of 3 :2.
Ans :
Terms of 3 :: 2 are 3 and 2.
Sum of these terms = 3 + 2 = 5
Sheela will get 
of total pens and Sangeeta
will get 
of total pens.
Number of pens with Sheela =
Number of pens with Sangeeta =
Q.15 : Mother wants to divide Rs 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.
Ans :
Ratio of ages =
Therefore, mother wants to divide Rs 36
in a ratio of 5 :: 4.
Terms of 5 :: 4 are 5 and 4.
Sum of these terms = 5 + 4 = 9
Shreya will get 
of the total money and
Bhoomika will get 
of it.
Amount that Shreya will get = 
Amount that Bhoomika will get = 
Therefore, Shreya and Bhoomika will get
Rs 20 and Rs 16 respectively.
Q.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.
Ans :
(a) Present age of father = 42 years
Present age of son = 14 years
Required ratio =
(b) Two years ago, the age of the son
was 12 years and the age of the father was 42 − 2 = 40 years
Required ratio =
(c) After 10 years, the age of the
father and son will be 52 years and 24 years respectively.
Required ratio =
(d) 12 years ago, the father was 30
years old.
At that time, age of son = 14 − 12
= 2 years
Required ratio =
Exercise 12.2
Q.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
Ans :
(a) 15, 45, 40, 120
Therefore, 15 : 45 = 40 : 120
Hence, these are in proportion.
(b) 33, 121, 9, 96
Therefore, 33 : 121 ≠ 9 : 96
Hence, these are not in proportion.
(c) 24, 28, 36, 48
Therefore, 24 : 28 ≠ 36 : 48
Hence, these are not in proportion.
(d) 32, 48, 70, 210
Therefore, 32 : 48 ≠ 70 : 210
Hence, these are not in proportion.
(e) 4, 6, 8, 12
Therefore, 4 : 6 = 8 : 12
Hence, these are in proportion.
(f) 33, 44, 75, 100
Therefore, 33 : 44 = 75 : 100
Hence, these are in proportion.
Q.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
Ans :
(a) 16 :: 24 :: : 20 :: 30
Therefore, 16 :: 24 = 20 :: 30
Hence, True
(b) 21 :: 6 :: : 35 :: 10
Therefore, 21 :: 6 = 35 :: 10
Hence, True
(c) 12 :: 18 :: : 28 :: 12
Therefore, 12 :: 18 ≠ 28 :: 12
Hence, False
(d) 8 :: 9 :: : 24 :: 27
As
,
Therefore, True
(e) 5.2 :: 3.9 :: : 3 :: 4
As 
,
Therefore, 5.2 :: 3.9 ≠ 3 :: 4
Hence, False
(f) 0.9 :: 0.36 :: : 10 :: 4
Therefore, 0.9 :: 0.36 = 10 :: 4
Hence, True
Q.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
Ans :
(a) 40 persons :: 200 persons = Rs 15 ::
Rs 75
True
(b) 7.5 l : 15 l =
5 kg : 10 kg
True
(c) 99 kg : 45 kg = Rs 44 : Rs 20
True
(d) 32 m : 64 m = 6 sec : 12 sec
True
(e) 45 km : 60 km = 12 hrs : 15 hrs
False
Q.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
Ans :
(a) 25cm : 1 m and Rs 40 : Rs 160
25 cm =
= 0.25 m
Yes. These are in proportion.
Middle terms are 1m, Rs 40.
Extreme terms are 25 cm, Rs 160.
(b) 39 l : 65 l and
6 bottles : 10 bottles
Yes. These are in proportion.
Middle terms are 65 l, 6
bottles.
Extreme terms are 39 l, 10
bottles.
(c) 2 kg : 80 kg and 25g : 625 g
No. These are not in proportion.
(d) 200 mL : 2.5 l and
Rs 4 : Rs 50
1 l = 1000 mL
2.5 l = 2500 mL
Yes. These are in proportion.
Middle terms are 2.5 l, Rs
4.
Extreme terms are 200 mL, Rs 50.
Exercise 12.3
Q.1 : If the cost of 7 m of cloth is Rs 294,
find the cost of 5 m of cloth.
Ans :
Cost of 7 m cloth = Rs 294
Cost of 1 m cloth =
Therefore, cost of 5 m cloth = 42 × 5 =
Rs 210
Q.2 : Ekta
earns Rs 1500 in 10 days. How much will she earn in 30 days?
Ans :
Money earned in 10 days = Rs 1500
Money earned in 1 day =
Therefore, money earned in 30 days =
150 × 30 = Rs 4500
Q.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.
Ans :
Measure of rain in 3 days = 276 mm
Measure of rain in 1 day =
Therefore, measure of rain in 7 days =
92 × 7 = 644 mm
Q.4 : Cost of 5 kg of wheat is Rs 30.50.
(a) What will be the cost of 8 kg of
wheat?
(b) What quantity of wheat can be
purchased in Rs 61?
Ans :
(a) Cost of 5 kg wheat = Rs 30.50
Cost of 1 kg wheat =
Therefore, cost of 8 kg wheat = 6.10 ×
8 = Rs 48.80
(b) Wheat purchased in Rs 30.50 = 5 kg
Wheat purchased in Re 1 =
Therefore, wheat purchased in Rs 61 =
= 10 kg
Q.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?
Ans :
Temperature drop in 30 days = 15°C
Temperature drop in 1 day =
Therefore, temperature drop in next 10
days =
Thus, there will be a temperature drop
of 5ºC in the next ten days.
Q.6 : Shaina pays Rs 7500 as rent for 3
months. How much does she has to pay for a whole year,
if the rent per month remains same?
Ans :
Rent for 3 months = Rs 7500
Rent for 1 month =
= Rs 2500
Therefore, rent for 12 months = 2500 ×
12 = 30000
Thus, she has to pay Rs 30000 for a
whole year.
Q.7 : Cost of 4 dozens
bananas is Rs 60. How many bananas can be purchased for Rs 12.50?
Ans :
Numbers of bananas bought in Rs 60 = 4
dozens = 4 × 12 = 48
Number of bananas bought in Re 1 =
Therefore, number of bananas bought in
Rs 12.50 =
= 10 bananas
Thus, 10 bananas can be purchased for
Rs 12.50.
Q.8 : The weight of 72 books is 9 kg. What is
the weight of 40 such books?
Ans :
Weight of 72 books = 9 kg
Weight of 1 book =
Therefore, weight of 40 books =
Thus, the weight of 40 such books is 5
kg.
Q.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?
Ans :
Diesel required for 594 km = 108 litres
Diesel required for 1 km =
=
Therefore, diesel required for 1650 km
=
= 300 litres
Thus, 300 litres diesel will be
required by the truck to cover a distance of 1650 km.
Q.10 : Raju purchases 10 pens for Rs 150 and
Manish buys 7 pens for Rs 84. Can you say who got the pens cheaper?
Ans :
Raju purchased 10 pens for Rs 150.
∴
Price of 1 pen =
Manish purchased 7 pens for Rs 84.
∴
Price of 1 pen =
Therefore, Manish got the pens cheaper.
Q.11 : Anish made 42 runs in 6 overs and Anup
made 63 runs in 7 overs. Who made more runs per over?
Ans :
Runs made by Anish in 6 overs = 42
∴
Runs made by Anish in 1 over =
Runs made by Anup in 7 overs = 63
∴
Runs made by Anup in 1 over = 
= 9
Clearly, Anup made more runs per over.
End of Questions