## NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion (Ex 12.2) Exercise 12.2

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## Access NCERT Solutions for Class 6 Maths Chapter 12- Ratio and Proportion

Exercise 12.2

Refer to pages 3-6 for exercise 12.2 in the PDF

1. Determine if the following are in proportion.

(a) 15, 45, 40, 120

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 15:45$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{15}}{{45}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{3}$

${\text{First term}}:{\text{Second term}} = 1:3$

Therefore,

$15:45 = 1:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 40:120$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{40}}{{120}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{3}$

${\text{Third term}}:{\text{Fourth term}} = 1:3$

Therefore,

$40:120 = 1:3$

Hence, 15, 45, 40, 120 are in proportion, since $15:45 = 1:3 = 40:120$.

(b) 33, 121, 9, 96

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 33:121$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{33}}{{121}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{{11}}$

${\text{First term}}:{\text{Second term}} = 3:11$

Therefore,

$33:121 = 3:11$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 9:96$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{9}{{96}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{{32}}$

${\text{Third term}}:{\text{Fourth term}} = 3:32$

Therefore,

$9:96 = 3:32$

Hence, 33, 121, 9, 96 are not in proportion, since $33:121 = 3:11 \ne 3:32 = 9:96$.

(c) 24, 28, 36, 48

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 24:28$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{24}}{{28}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{6}{7}$

${\text{First term}}:{\text{Second term}} = 6:7$

Therefore,

$24:28 = 6:7$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 36:48$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{36}}{{48}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{4}$

${\text{Third term}}:{\text{Fourth term}} = 3:4$

Therefore,

$36:48 = 3:4$

Hence, 24, 28, 36, 48 are not in proportion, since $24:28 = 6:7 \ne 3:4 = 36:48$.

(d) 32, 48, 70, 210

${\text{First term}}:{\text{Second term}} = 32:48$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{32}}{{48}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore,

$32:48 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 70:210$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{70}}{{210}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{3}$

${\text{Third term}}:{\text{Fourth term}} = 1:3$

Therefore,

$70:210 = 1:3$

Hence, 32, 48, 70, 210are not in proportion, since $32:48 = 2:3 \ne 1:3 = 70:210$.

(e) 4, 6, 8, 12

${\text{First term}}:{\text{Second term}} = 4:6$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{4}{6}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore,

$4:6 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 8:12$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{8}{{12}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{2}{3}$

${\text{Third term}}:{\text{Fourth term}} = 2:3$

Therefore,

$8:12 = 2:3$

Hence, 4, 6, 8, 12are in proportion, since $4:6 = 2:3 = 8:12$.

(f) 33, 44, 75, 100

${\text{First term}}:{\text{Second term}} = 33:44$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{33}}{{44}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{4}$

${\text{First term}}:{\text{Second term}} = 3:4$

Therefore,

$33:44 = 3:4$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 75:100$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{75}}{{100}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{4}$

${\text{Third term}}:{\text{Fourth term}} = 3:4$

Therefore,

$75:100 = 3:4$

Hence, 33, 44, 75, 100are in proportion, since $33:44 = 3:4 = 75:100$.

2. Write True (T) or False ( F ) against each of the following statements :

(a) $16:24::20:30$

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 16:24$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{16}}{{24}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore,

$16:24 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 20:30$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{20}}{{30}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{2}{3}$

${\text{Third term}}:{\text{Fourth term}} = 2:3$

Therefore,

$20:30 = 2:3$

Since $16:24 = 2:3 = 20:30$, then $16:24$ and $20:30$ are in proportion. And consequently, the given statement $16:24::20:30$ is true.

(b) $21:6::35:10$

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 21:6$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{21}}{6}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{7}{2}$

${\text{First term}}:{\text{Second term}} = 7:2$

Therefore,

$21:6 = 7:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 35:10$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{35}}{{10}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{7}{2}$

${\text{Third term}}:{\text{Fourth term}} = 7:2$

Therefore,

$35:10 = 7:2$

Since $21:6 = 7:2 = 35:10$, then $21:6$ and $35:10$ are in proportion. And consequently, the given statement $21:6::35:10$ is true.

(c) \[12:18::28:12\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 12:18$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{12}}{{18}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore,

$12:18 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 28:12$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{28}}{{12}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{7}{3}$

${\text{Third term}}:{\text{Fourth term}} = 7:3$

Therefore,

$28:12 = 7:3$

Since $12:18 = 2:3 \ne 7:3 = 28:12$, then $12:18$ and $28:12$ are not in proportion. And consequently, the given statement \[12:18::28:12\] is false.

(d) \[8:9::24:27\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 8:9$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{8}{9}$

${\text{First term}}:{\text{Second term}} = 8:9$

Therefore,

$8:9 = 8:9$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 24:27$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{24}}{{27}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{8}{9}$

${\text{Third term}}:{\text{Fourth term}} = 8:9$

Therefore,

$24:27 = 8:9$

Since $8:9 = 8:9 = 24:27$, then $8:9$ and $24:27$ are in proportion. And consequently, the given statement \[8:9::24:27\] is true.

(e) \[5.2:3.9::3:4\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 5.2:3.9$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{5.2}}{{3.9}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{52}}{{39}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{4}{3}$

${\text{First term}}:{\text{Second term}} = 4:3$

Therefore,

$5.2:3.9 = 4:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 3:4$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{4}$

${\text{Third term}}:{\text{Fourth term}} = 3:4$

Therefore,

\[3:4 = 3:4\]

Since $5.2:3.9 = 4:3 \ne 3:4 = 3:4$, then $5.2:3.9$ and $3:4$ are not in proportion. And consequently, the given statement \[5.2:3.9::3:4\] is false.

(f) \[0.9:0.36::10:4\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 0.9:0.36$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{0.9}}{{0.36}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{90}}{{36}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{5}{2}$

${\text{First term}}:{\text{Second term}} = 5:2$

Therefore,

$0.9:0.36 = 5:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 10:4$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{10}}{4}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{5}{2}$

${\text{Third term}}:{\text{Fourth term}} = 5:2$

Therefore,

$10:4 = 5:2$

Since $0.9:0.36 = 5:2 = 10:4$, then $0.9:0.36$ and $10:4$ are in proportion. And consequently, the given statement \[0.9:0.36::10:4\] is true.

3. Are the following statements true?

(a) 40 persons : 200 persons = ₹ 15 : ₹ 75

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 40:200$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{40}}{{200}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{5}$

${\text{First term}}:{\text{Second term}} = 1:5$

Therefore,

$40:200 = 1:5$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 15:75$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{15}}{{75}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{5}$

${\text{Third term}}:{\text{Fourth term}} = 1:5$

Therefore,

$15:75 = 1:5$

Since $40:200 = 1:5 = 15:75$, then the given statement is true.

(b) $7.5$litres : 15 litres = 5 kg : 10 kg

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 7.5:15$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{75}}{{150}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{2}$

${\text{First term}}:{\text{Second term}} = 1:2$

Therefore,

$7.5:15 = 1:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 5:10$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{5}{{10}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{2}$

${\text{Third term}}:{\text{Fourth term}} = 1:2$

Therefore,

$5:10 = 1:2$

Since $7.5:15 = 1:2 = 5:10$, then the given statement is true.

(c) 99 kg : 45 kg = ₹ 44 : ₹ 20

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 99:45$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{99}}{{45}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{11}}{5}$

${\text{First term}}:{\text{Second term}} = 11:5$

Therefore,

$99:45 = 11:5$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 44:20$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{44}}{{20}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{11}}{5}$

${\text{Third term}}:{\text{Fourth term}} = 11:5$

Therefore,

$44:20 = 11:5$

Since $99:45 = 11:5 = 44:20$, then the given statement is true.

(d) 32 m : 64 m = 6 sec : 12 sec

Ans:In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 32:64$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{32}}{{64}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{2}$

${\text{First term}}:{\text{Second term}} = 1:2$

Therefore,

$32:64 = 1:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 6:12$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{6}{{12}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{2}$

${\text{Third term}}:{\text{Fourth term}} = 1:2$

Therefore,

$6:12 = 1:2$

Since $32:64 = 1:2 = 6:12$, then the given statement is true.

(e) 45 km : 60 km = 12 hours : 15 hours

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 45:60$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{45}}{{60}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{4}$

${\text{First term}}:{\text{Second term}} = 3:4$

Therefore,

$45:60 = 3:4$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 12:15$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{12}}{{15}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{4}{5}$

${\text{Third term}}:{\text{Fourth term}} = 4:5$

Therefore,

$12:15 = 4:5$

Since $45:60 = 3:4 \ne 4:5 = 12:15$, then the given 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 ₹ 40 : ₹ 160

Ans: 1 m can be written as $1{\text{ m}} = 100{\text{ cm}}$.

Therefore the first ratio can be written as, $25{\text{ cm}}:1{\text{ m}} = 25{\text{ cm}}:100{\text{ cm}}$.

In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 25:100$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{25}}{{100}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{4}$

${\text{First term}}:{\text{Second term}} = 1:4$

Therefore,

$25:100 = 1:4$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 40:160$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{40}}{{160}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{4}$

${\text{Third term}}:{\text{Fourth term}} = 1:4$

Therefore,

$40:160 = 1:4$

Since $25:100 = 1:4 = 40:160$, the given ratios are in proportions.

If $a:b$ and $c:d$ are two ratios in proportions then $a,{\text{ }}d$ are the extreme terms and $b,{\text{ }}c$ are the middle terms.

Therefore, from the given ratios 1 m,₹ 40are the middle terms and 25 cm, ₹ 160 are the extreme terms.

(b) 39 litres : 65 litres and 6 bottles : 10 bottles

Ans: In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 39:65$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{39}}{{65}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{5}$

${\text{First term}}:{\text{Second term}} = 3:5$

Therefore,

$39:65 = 3:5$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 6:10$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{6}{{10}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{5}$

${\text{Third term}}:{\text{Fourth term}} = 3:5$

Therefore,

$6:10 = 3:5$

Since $39:65 = 3:5 = 6:10$, the given ratios are in proportions.

If $a:b$ and $c:d$ are two ratios in proportions then $a,{\text{ }}d$ are the extreme terms and $b,{\text{ }}c$ are the middle terms.

Therefore, from the given ratios 65 litres, 6 bottles are the middle terms and 39 litres, 10 bottles are the extreme terms.

(c) 2 kg : 80 kg and 25 g : 625 g

Ans: In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 2:80$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{{80}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{{40}}$

${\text{First term}}:{\text{Second term}} = 1:40$

Therefore,

$2:80 = 1:40$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 25:625$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{25}}{{625}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{{25}}$

${\text{Third term}}:{\text{Fourth term}} = 1:25$

Therefore,

$25:125 = 1:25$

Since $2:80 = 1:40 \ne 1:25 = 25:625$, the given ratios are not in proportions.

(d) 200 ml :$2.5$ litre and ₹ 4 : ₹ 50

Ans: 1 litre can be written as $1{\text{ litre}} = 1000{\text{ mL}}$.

Therefore,

$2.5{\text{ litre}} = 2.5 \times 1000{\text{ ml}}$

$2.5{\text{ litre}} = 2500{\text{ ml}}$

Therefore the first ratio can be written as, \[200{\text{ ml}}:2.5{\text{ litre}} = 200{\text{ ml}}:2500{\text{ ml}}\].

In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 200:2500$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{200}}{{2500}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{{25}}$

${\text{First term}}:{\text{Second term}} = 2:25$

Therefore,

$200:2500 = 2:25$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 4:50$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{4}{{50}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{2}{{25}}$

${\text{Third term}}:{\text{Fourth term}} = 2:25$

Therefore,

$4:50 = 2:25$

Since $200:2500 = 2:25 = 4:50$, the given ratios are in proportions.

If $a:b$ and $c:d$ are two ratios in proportions then $a,{\text{ }}d$ are the extreme terms and $b,{\text{ }}c$ are the middle terms.

Therefore, from the given ratios $2.5$ litres, ₹ 4are the middle terms and 200 ml, ₹ 50 are the extreme terms.

## NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2

Opting for the NCERT solutions for Ex 12.2 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 12.2 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 12 Exercise 12.2 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 6 Maths Chapter 12 Exercise 12.2, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.

Do not delay any more. Download the NCERT solutions for Class 6 Maths Chapter 12 Exercise 12.2 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.

1. How many questions are present in NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion?

Class 6 Maths Chapter 12 'Ratio and proportion' consists of three exercises in total -

There are 16 questions in Exercise 12.1. These questions are based on calculating ratios.

There are four questions in Exercise 12.2. These are short answer type questions, majorly objective ones.

Lastly, there are 11 questions in Exercise 12.3. These questions are short and long answer types that ask for the application of the unitary method.

2. What is the unitary method in Class 6 Maths Chapter 12?

The Unitary Method is a method that involves determining the value of one unit first and then determining the value of the requisite number of units.

**For Example:**

Q. If the cost of six chocolates is Rs. 30, then how much will 20 chocolates cost?

**Solution:** Cost of six chocolates = Rs.30

Cost of one chocolate = 30/6 = Rs.5

Therefore,

Cost of 20 chocolates = 20 x 5

= Rs.100

3. What are the essential concepts explained in Class 6 Maths Chapter 12?

Class 6 Maths Chapter 12 covers topics like calculating ratios, finding the proportion of two ratios, and solving problems using unitary methods. These principles are essential, not only for Class 6 but also for higher classes. As a result, make sure you understand these fundamental principles as soon as possible. You can thorough these topics by solving NCERT questions with the help of Vedantu’s Chapter 12 NCERT Solutions.

4. Can I avail NCERT Solutions for Class 6 Maths Chapter 12 for free?

Yes, absolutely you can avail the NCERT Solutions for Class 6 Maths Chapter 12 free of cost on Vedantu. All you have to do is visit the official website or download the Vedantu app where you can find the NCERT solutions to all the exercises of Chapter 12 'Ratio and Proportion' in PDF format. You can download these solutions on your device free of charge.

5. How to solve difficult questions of Class 6 Maths Chapter 12?

Some students may find the questions in Class 6 Maths Chapter 12 challenging to answer. There's nothing to be worried about. Everything is doable if you put in the effort and practice. Try to figure out where you're having the most problems. After you've grasped the concept, you can go on to the more important questions. Practice the questions numerous times until you feel confident about them.