NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.2

NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.2 Proportion

Find here step by step NCERT Solutions For Class 6 Maths Exercise 12.2 from Chapter 12 Ratio and Proportion. NCERT solutions for Class 6 Maths Exercise 12.2 deals with the concept of Proportion.

Prerequisite / Revise this :

NCERT Solutions for Class 6 Maths Chapter 12 Ex 12.2

• Four quantities are said to be in Proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.

Example – 2, 7, 6, 21 are in proportion, since 2/7 = 6/21.

• We indicate the proportion by :: , so proportion in above example can be written as 2 : 7 :: 6 : 21, it is read as 2 is to 7 as 6 is to 21.

• In a statement of proportion, the four quantities involved when taken in are known as respective terms.

• First and fourth terms are known extreme terms. Second and third terms are known as middle terms. In the above proportion, 2 and 21 are the extreme terms and 7 and 6 are the middle terms.

• The order of terms in the proportion is important. 2, 7, 6 and 21 are in proportion, but 2, 7, 21 and 6 are not, since 2/7 is not equal to 21/6.

EXERCISE 12.2
Finding Proportion

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

ANSWER

(a) Ratio of 15 to 45 = \frac{15}{45} = 1 : 3

Ratio of 40 to 120 = \frac{40}{120} = 1 : 3

Since, 15 : 45 = 40 : 120
Therefore, 15, 45, 40 and 120 are in proportion.

(b) Ratio of 33 to 121 = \frac{33}{121} = 3 : 11

Ratio of 9 to 96 = \frac{3}{32} = 3 : 32

Since, 33 : 121 \neq 9 : 96
Therefore, 33, 121, 9 and 96 are not in proportion.

(c) Ratio of 24 to 28 = \frac{24}{28} = 6 : 7

Ratio of 36 to 48 = \frac{36}{48} = 3 : 4

Since, 24 : 28 \neq 36 : 48
Therefore, 15, 45, 40 and 120 are not in proportion.

(d) Ratio of 32 to 48 = \frac{32}{48} = 2 : 3

Ratio of 70 to 210 = \frac{70}{210} = 1 : 3

Since, 32 : 48 \neq 70 : 210
Therefore, 32, 48, 70 and 210 are not in proportion.

(e) Ratio of 4 to 6 = \frac{4}{6} = 2 : 3

Ratio of 8 to 12 = \frac{8}{12} = 2 : 3

Since, 4 : 6 = 8 : 12
Therefore, 4, 6, 8 and 12 are in proportion.

(f) Ratio of 33 to 44 = \frac{33}{44} = 3 : 4

Ratio of 75 to 100 = \frac{75}{100} = 3 : 4

Since, 33 : 44 = 75 : 100
Therefore, 33, 44, 75 and 100 are in proportion.

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

ANSWER

(a) 16 : 24 = 2 : 3
and 20 : 30 = 2 : 3

So, 16 : 24 = 20 : 30
Hence 16 : 24 :: 20 : 30 is true.

(b) 21 : 6 = 7 : 2
and 35 : 10 = 7 : 2

So, 21 : 6 = 35 : 10
Hence 21 : 6 :: 35 : 10 is true.

(c) 12 : 18 = 2 : 3
and 28 : 12 = 7 : 3

So, 12 : 18 \neq 28 : 12
Hence 12 : 18 :: 28 : 12 is false.

(d) 8 : 9 is in simplest form,
and 24 : 27 = 8 : 9

Hence 8 : 9 :: 24 : 27 is true.

(e) 5.2 : 3.9 = 4 : 3
and 3 : 4 is in simplest form,

So, 5.2 : 3.9 \neq 3 : 4
Hence 5.2 : 3.9 :: 3 : 4 is false.

(f) 0.9 : 0.36 = 5 : 2
and 10 : 4 = 5 : 2

So, 0.9 : 0.36 = 10 : 4
Hence 0.9 : 0.36 :: 10 : 4 is true.

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

ANSWER

(a) 40 persons : 200 persons = 1 : 5
and ₹ 15 : ₹ 75 = 1 : 5

Therefore, given statement is true.

(b) 7.5 litres : 15 litres = 1 : 2
and 5 kg : 10 kg = 1 : 2

Therefore, given statement is true.

(c) 99 kg : 45 kg = 9 : 5
and ₹ 44 : ₹ 20 = 11 : 5

Therefore, given statement is false.

(d) 32 m : 64 m = 2 : 4
and 6 sec : 12 sec = 1 : 2

Therefore, given statement is false.

(e) 45 km : 60 km = 3 : 4
and 12 hours : 15 hours = 4 : 5

Therefore, 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 ₹ 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 litre and ₹ 4 : ₹ 50

ANSWER

(a) 25 cm : 1 m = 25 cm : 100 cm = 1 : 4

and ₹ 40 : ₹ 160 = 1 : 4

Since, both ratios are equal, they form a proportion,

Middle term = 1 m and ₹ 40
Extreme terms = 25 cm and ₹ 160

(b) 39 litres : 65 litres = 3 : 5

and 6 bottles : 10 bottles = 3 : 5

Since, both ratios are equal, they form a proportion,

Middle term = 65 litres and 6 bottles
Extreme terms = 39 litres and ₹ 10 bottles

(c) 2 kg : 80 kg = 1 : 40

and 25 g : 625 g = 1 : 25

Since, ratios are not equal, they do not form proportion.

(d) 200 ml : 2.5 litre = 200 ml : 2500 ml = 2 : 25

and ₹ 4 : ₹ 50 = 2 : 25

Since, both ratios are equal, they form a proportion,

Middle term = 2.5 litre and ₹ 4
Extreme terms = 200 ml and ₹ 25

NCERT SOLUTIONS FOR CLASS 6 MATHS CHAPTER 12 RATIO AND PROPORTION

Check NCERT Solutions of other exercises from Class 6 Maths Chapter 12 Ratio and Proportion by clicking the links given below.

Exercise 12.1
Exercise 12.2
Exercise 12.3

We hope Ncert Solutions for class 6 Maths Exercise 12.2 has helped you understand how to find Proportion.

Write in the comment section for any error or any solution related queries from the exercise. [ Ncert Solutions for Class 6 Maths Exercise 12.2 ]

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